Publications by Pavel Kurasov

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I Books

  1. Singular perturbations of differential operators.
    Solvable Schrödinger type operators
    (with S.Albeverio) Cambridge Univ. Press, Cambridge, 429p., 2000
    (London Mathematical Society Lecture Notes 271). Preface
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    II Editorial work

  2. Operator Methods in Ordinary and Partial Differential Equations
    Proceedings of the Sonja Kovalevsky symposium held in the University of Stockholm, June 16-22, 2000
    (with S.Albeverio, N.Elander and W.N.Everitt) Operator Theory: Advances and Applications, 132 , 2002. Preface
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  3. Spectral Methods for Operators of Mathematical Physics
    Proceedings of the conference held in Bedlewo Math. Center, Poland, May 13-18, 2002
    (with J.Janas and S.Naboko) Operator Theory: Advances and Applications, 154 , 2004.
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  4. Operator Theory, Analysis and Mathematical Physics
    Proceedings of the conference held in Bedlewo Math. Center, Poland, July 6-11, 2004
    (with J.Janas, A.Laptev, S.Naboko, and G.Stolz) Operator Theory: Advances and Applications, 174 , 2007.
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  5. Methods of Spectral Analysis in Mathematical Physics
    Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006, Lund, Sweden
    (with J.Janas, A.Laptev, S.Naboko, and G.Stolz) Operator Theory: Advances and Applications, 186 , 2009.
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  6. Spectral Theory and Analysis
    Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2008, Bedlewo, Poland
    (with J.Janas, A.Laptev, S.Naboko, and G.Stolz) Operator Theory: Advances and Applications, 214 , 2011.
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  7. Operator Methods in Mathematical Physics
    Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Sweden
    (with J.Janas, A.Laptev, and S.Naboko) Operator Theory: Advances and Applications, 227 , 2013.
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    8. imp The files can be downloaded from this WWW-page for personal use only!
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    kurasov@math.su.se

    III PhD theses

  8. Wave-guide bands of continuous spectrum
    PhD Thesis, Dept. of Mathematical Physics, Leningrad Univ., Leningrad, 1989.

  9. On direct and inverse scattering problems in dimension one
    PhD Thesis, Stockholm University, ISSN-91-7153-162-9, Akademitryck AB, Edsbruk, Sweden, 1993.

    IV Papers in journals

  10. An electron in a Homogeneous Crystal of Point Atoms with Internal Structure II
    (with B.S.Pavlov) Teor.i Mat. Fiz., 74 (1988), 82-93. PDF file

  11. A one-electron model of a Long Molecule
    Leningrad Univ. Vestnik, ser.4, 3 (nr.18),(1989), 8-15 (In Russian).

  12. Connexions and Effective S-matrix in Triangle Representation for Quantum Scattering
    (with Yu.A.Kuperin, Yu.B.Melnikov, S.P.Merkuriev) Annals of Physics(NY), 205 (1991), 330-361. PDF file

  13. Resonances and irreversibility for Schroedinger evolution
    (with N.Elander, B.S.Pavlov) International Journal of Quantum Chemistry, 46 (1993), 401-414.

  14. Complex scaling and selfadjoint dilations
    (with N.Elander) International Journal of Quantum Chemistry, 46 (1993), 415-418. PDF file

  15. Zero-range potentials with internal structures and the inverse scattering problem
    Let. Math. Phys., 25 (1992), 287-297. PDF file

  16. On the delta'-interaction arizing in the exterior complex scaling
    (with A.Scrinzi and N.Elander) Phys. Rev A, 49 (1994), 5095-5097. PDF file

  17. Distribution theory for discontinuous test functions and differential operators with generalized coefficients
    J.Math.Anal.Appl., 201 (1996), 297-323. PDF file

  18. Doubly periodical in time and energy exactly soluble system with two interacting systems of states
    (with Yu.N.Demkov, V.N.Ostrovsky) J. Phys. A: Math. Gen., 28 (1995), 4361-4380. PDF file

  19. Scattering matrices with finite phase shift and the inverse scattering problem
    Inverse Problems, 12 (1996), 295-307. PDF file

  20. On the Coulomb potential in dimension one
    J. Phys. A: Math. Gen., 29 (1996), 1767-1771. PDF file

  21. Rank one perturbations, approximations and selfadjoint extensions
    (with S.Albeverio) J. Func. Anal., 148 (1997), 152-169. PDF file

  22. Energy dependent boundary conditions and few-body scattering problem
    Rev. Math. Phys., 9 (1997), 853-906. PDF file

  23. Finite rank singular perturbations and distributions with discontinuous testfunctions
    (with J.Boman) Proceedings of AMS, 126 (1998), 1673--1683. PDF file

  24. Rank one perturbations of not semibounded operators
    (with S.Albeverio) Integr. Equ. Oper. Theory, 27 (1997), 379-400. PDF file

  25. S-matrix, resonances, and wavefunctions for transport through billiards with leads
    (with S.Albeverio, F.Haake, M.Kus, P.Seba) J. Math. Phys., 37 (1996), 4888-4903. PDF file

  26. Pseudo-differential operators with point interactions
    (with S.Albeverio) Let. Math. Phys., 41 (1997), 79-92. PDF file

  27. Response to "Comment on 'On the Coulomb potential in one dimension' " by W.Fisher, H.Leschke and P.Muller
    J. Phys. A: Math. Gen., 30 (1997), 5583-5589. PDF file
    See also related article by W.Fisher, H.Lescke and P.Muller PDF file

  28. Symmetries of Schrödinger operator with point interactions
    (with S.Albeverio and L.Dabrowski) Let. in Math. Phys., 45 (1998), 33-47. PDF file

  29. Finite rank perturbations and distribution theory
    (with S.Albeverio) Proc. AMS, 127 , 1151--1161, 1999. PDF file

  30. Inverse scattering transformation for positons
    (with K.Packalen) J.Phys.A:Math.Gen., 32 (1999), 1269--1278. PDF file

  31. Many body problems with ``spin''-related contact interactions
    (with S.Albeverio and S-M.Fei) Reports in Mathematical Physics, 47 (2001), 157--165. PDF file

  32. Spectral asymptotics for Schrödinger operators with periodic point interactions
    (with J.Larson) J. Math. Anal. Appl., 266 (2002), 127--148. PDF file

  33. On the inverse scattering problem on branching graphs
    (with F.Stenberg) J.Phys.A: Math. Gen., 35 , (2002), 101--121. PDF file

  34. On approximations of rank one H_{-2}-perturbations
    (with S.Albeverio, L.Nizhnik and V.Koshmanenko) Proc. AMS., 131 (2003), 1443--1452 PDF file

  35. Point interactions: PT-Hermiticity and reality of the spectrum
    (with S.Albeverio and S.-M.Fei) Letters in Math. Phys., 59 (2002), 227-242. PDF file

  36. H_{-n}-perturbations of self-adjoint operators and Krein's resolvent formula
    Integr.Eq.Oper.Theory., 45 (2003), 437-460 PDF file

  37. On the essential spectrum of a class of singular matrix differential operators. I Quasiregularity conditions and essential self-adjointness
    (with S.Naboko) Mathematical Physics, Analysis and Geometry, 5 (2002), 243-286 PDF file

  38. Krein's formula and perturbation theory
    (with S.T.Kuroda) Journal of Operator Theory, 51 (2004), 321-334. PDF file

  39. On field theory methods in singular perturbation theory
    (with Yu.Pavlov), Letters in Mathematical Physics, 64 (2003), 171-184 PDF file

  40. Gauge fields, point interactions and few-body problems in one dimension
    (with S.Albeverio and Sh-M.Fei) Rep. Math. Phys., 53 (2004), 363-370
    (SFB256 - Preprint Nr.614, Rheinische Friedrich-Wilhelms-Universität-Bonn, September 1999). PDF file

  41. Symmetries of quantum graphs and the inverse scattering problem
    (with J.Boman) Adv. Appl. Math., 35 (2005), 58-70. PDF file

  42. Finite speed of propagation and local boundary conditions for wave equations with point interactions
    (with A.Posilicano) Proc. AMS, 133 (2005), 3071-3078. PDF file

  43. High order singular rank one perturbations of a positive operator
    (with A.Dijksma and Yu.Shondin) Integral Equations Operator Theory, 53 (2005), 209-245.
    PDF file

  44. Inverse spectral problem for quantum graphs
    (with M.Nowaczyk) J. Phys. A: Mathematical and General, 38 (2005), 4901-4915 PDF file
    Correction: J. Phys. A: Mathematical and General, 39 (2006), 993 PDF file

  45. Reflectionless Potentials and Point Interactions in Pontryagin Spaces
    (with A.Luger) Lett. Math. Phys., 73 (2005), 109--122. PDF file

  46. Wigner-von Neumann Perturbations of a Periodic Potential:
    Spectral Singularities in Bands
    (with S.Naboko) Math. Proc. Cambridge Philosophical Society, 142 (2007), 161
    PDF file

  47. On the essential spectrum of a class of singular matrix differential operators II. Weyl's limit circles for Hain-Lust operator whenever quasiregularity conditions are not satisfied
    (with I.Lelyavin and S.Naboko) Proceedings A (Mathematics) Royal Society of Edinburg 138A (2008), 109-138 PDF file

  48. Graph Laplacians and Topology
    Arkiv för Matematik 46 (2008), 95--111 PDF file

  49. von Neumann-Wigner Theorem: level's repulsion and degenerate eigenvalues
    (with Yu.N.Demkov), Theor. and Mathematical Physics, 153 (2007), 68-85; PDF file in Russian
    English translation 153 (2007) 1407-1422 PDF file

  50. Inverse problems for quantum trees
    (with S.Avdonin), Inverse Problems and Imaging, 2 (2008), 1- 21 PDF file

  51. Schrödinger operators on graphs and geometry I: Essentially bounded potentials
    J.Func. Anal. 254 (2008), 934-953 PDF file

  52. Triplet extensions I: semibounded operators in the scale of Hilbert spaces
    J. Anal. Math., 107 (2009), 251-286 PDF file.

  53. How to model $p$-scattering using point interactions and related problems
    Few-body Systems, 45 (2009), 187-190, PDF file
    The original publication is available at www.springerlink.com , DOI: 10.1007/s00601-009-0025-8

  54. On the Inverse Problem for Quantum Graphs with One Cycle
    Acta Physica Polonica A, 116 (2009), 765-771, PDF file
    The original publication is available at http://przyrbwn.icm.edu.pl/APP/PDF/116/a116z506.pdf

  55. Inverse problem for Aharonov-Bohm rings
    Math. Proc. Cambridge Philosophical Society, First View Articles, 148 (2010), 331-362. PDF file
    The original publication is available at journals.cambridge.org, DOI:10.1017/S030500410999034X

  56. Geometric properties of quantum graphs and vertex scattering matrices
    (with M.Nowaczyk) Opuscula Mathematica, 30/3 (2010), 295-309 PDF file
    The original publication is available at http://www.opuscula.agh.edu.pl/, http://www.opuscula.agh.edu.pl/vol30/3/art/opuscula_math_3023.pdf

  57. Weyl-Titchmarsh type formula for periodic Schrödinger operator with Wigner-von Neumann potential
    (with S.Simonov) Proc. Roy. Soc. Edinburgh Sect. A , 143 (2013), 401-425. PDF file
    The original publication is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8862940&fileId=S0308210510001666

  58. Inverse Problems for Quantum Trees II
    Recovering Matching Conditions for Star Graphs
    (with S.Avdonin and M.Nowaczyk) Inverse Problems and Imaging, 4/4 (2010), 579-598 PDF file
    The original publication is available at http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5503

  59. An Operator Theoretic Interpretation of the Generalized Titchmarsh-Weyl Coefficient for a Singular Sturm-Liouville Problem
    (with A.Luger) Mathematical Physics, Analysis and Geometry, 14 , 115-151 (2011). PDF file
    The original publication is available at http://www.springerlink.com/content/j0727266082nnt11/ DOI 10.1007/s11040-011-9090-6

  60. Inverse Problems for Quantum Graphs: Recent Developments and Perspectives
    Acta Physica Polonica A, 120 , v6A (2011), 132-141 PDF file
    The original publication is available at http://przyrbwn.icm.edu.pl/APP/PDF/120/a120z6ap58.pdf

  61. Aharonov-Bohm ring touching a quantum wire: how to model it and to solve the inverse problem
    (with M.Enerback) Reports on Mathematical Physics, 68 n 3 (2011) 271-287 PDF file
    The original publication is available at http://www.sciencedirect.com/science/journal/00344877?oldURL=y

  62. Inverse problems for quantum graphs: recent developments and perspectives
    Acta Physica Polonica A, 120 (2012), A132-141. PDF file
    The original publication is available at http://przyrbwn.icm.edu.pl/APP/PDF/120/a120z6ap58.pdf

  63. Inverse scattering for lasso graph
    J.Math.Phys. 54 , 042103 (2013) PDF file
    The original publication is available at http://scitation.aip.org.ezp.sub.su.se/docserver/fulltext/aip/journal/jmp/54/4/1.4799034.pdf?expires=1434734229&id=id&accname=2090039&checksum=6DDD28F2255C802C5C50DF06C8862204

  64. Rayleigh estimates for differential operators on graphs
    (with S.\,Naboko) J.Spectral Theory, 4 (2014), 1Ð9; PDF file
    The original publication is available at http://www.ems-ph.org.ezp.sub.su.se/journals/show_abstract.php?issn=1664-039X&vol=4&iss=2&rank=1

  65. Can one distinguish quantum trees from the boundary?
    Proc. AMS, Posted October 26, 2011 . PDF file
    The original publication is available at http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2011-11077-3/home.html 

  66. Spectral Gap for Quantum Graphs and Their Edge Connectivity
    (with G.Malenova and S.Naboko) J.Phys.A:Math.Theor., 46 (2013), 275309 PDF file
    The original publication is available at http://stacks.iop.org/1751-8121/46/275309

  67. On refectionless equi-transmitting matrices
    (with R. Ogik and A. Rauf) Opuscula Math. 34, no. 3 (2014), 483501 PDF file
    The original publication is available at http://dx.doi.org/10.7494/OpMath.2014.34.3.483

  68. On the Spectral Gap for Laplacians on Metric Graphs
    Acta Physica Polonica A, 124 (2013), 1060-1062 PDF file
    The original publication is available at http://przyrbwn.icm.edu.pl/APP/PDF/124/a124z6p53.pdf

  69. On vertex conditions for elastic systems
    (with J-C. Kiik and M. Usman) Physics Letters A 379 , Issues 34-35, 18 September 2015, Pages 1871--1876
    PDF file
    The original publication is available at http://www.sciencedirect.com/science/article/pii/S0375960115004338
    (Research Report in Mathematics, N1 2015, Dept. of Mathematics, Stockholm Univ. . PDF file)

  70. Schrödinger operators on graphs: symmetrization and Eulerian cycles
    (with G. Karreskog and I.Trygg Kupersmidt) accepted for publication in Proc. AMS
    (Research Report in Mathematics, N3 2015, Dept. of Mathematics, Stockholm Univ. . PDF file)

  71. Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions
    (with Andrea Serio) accepted for publication in Nanosystems: Mathematics, Physics and Chemistry
    (Research Report in Mathematics, N4 2015, Dept. of Mathematics, Stockholm Univ. . PDF file)

    72. imp The files can be downloaded from this WWW-page for personal use only!
    I'll appreciate if you will send me an e-mail after downloading files:
    kurasov@math.su.se

    V Papers in proceedings of conferences

    A. Refereed volumes

  72. Surfaces with an Internal Structure
    (with B.S.Pavlov) In: P.Exner, P.Seba (eds) "Applications of Self-Adjoint Extensions in Quantum Physics" (Proc. Dubna, USSR, 1987), Springer-Verlag, Berlin, 1989 (Lectures Notes in Physics nr. 324). PDF file

  73. Three One-dimensional Bosons with an Internal Structure
    In: P.Exner, P.Seba (eds) "Schroedinger Operators, Standard and Nonstandard" (Proc. Dubna, USSR, 1988), World Scientific, Singapore,1989.

  74. Localization Effects in Non-Homogeneous Dielectrics
    (with B.S.Pavlov) Operator Theory: Advances and Applications, 46 (1990), 307-313.

  75. Inverse scattering problem on the half line and positon solutions of the KdV equation
    J.Tech.Phys., 37 (1996) 503-507. PDF file

  76. Scattering from impurity: Lax-Phillips approach
    Operator Theory: Advances and Applications, 123 (2001), 413-431. PDF file

  77. Generalized perturbations and operator relations
    (with B.Pavlov) In: Generalized functions, operator theory, and dynamical systems (Brussels, 1997), 345--353, Chapman & Hall/CRC, Boca Raton. PDF file

  78. Few-body Krein's formula
    (with B.S.Pavlov) Operator theory: Advances and Applications, 118 , (2000), 225-254. PDF file

  79. Scattering problem with physical behavior of scattering matrix and operator relations
    (with B.Pavlov). Operator theory: Advances and Applications, 113 (2000), 195--204. PDF file

  80. Singular cluster interactions in few-body problems
    (with S.Albeverio) Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998), 277--292, Lecture Notes in Pure and Appl. Math., 215, Dekker, New York, 2001. PDF file

  81. On rank one H_{-3} perturbations of positive self--adjoint operators
    (with K.Watanabe). In: F.Gesztesy, H.Holden, J.Jost, S.Paycha, M.Röckner, S.Scarlatti (Eds.), Stochastic Processes, Physics and Geometry: New Interplays. II, CMS conference proceedings, {\bf 29}, AMS, Providence, 2000, pp. 413-422. PDF file

  82. On H_{-4}-perturbations of self-adjoint operators
    (with K.Watanabe) Operator theory: Advances and Applications, 126 (2001), 179--196 (Proceedings of PDE-2000 conference in Clausthal). PDF file

  83. On Integrability of Many-Body Problems with Point Interactions
    (with S.Albeverio and Sh.-M.Fei) Operator theory: Advances and Applications, 132 (2002), 67-76 (Proceedings of S.Kovalevsky symposium, Stockholm 2000). PDF file

  84. Essential Spectrum Due to Singularity
    (with S.Naboko) In: J. Nonlinear Mathematical Physics, 2003. PDF file

  85. Singular and supersingular perturbations: Hilbert space methods
    Contemporary Mathematics, 340, Lecture Notes from a Workshop on Schrödinger Operator Theory, R. del Rio and C.Villegas-Blas (eds.), 185-216
    (Preprint Nr.16, Dept. of Mathematics, Lund Inst. of Technology, 2003). PS file (PDF file)

  86. Spectral gap for complete graphs: upper and lower estimates
    accepted for publication in Proceedings of the conference, Bielefeld, december 2013. D.Mugnolo (ed.),
    (Research Report in Mathematics, N2 2015, Dept. of Mathematics, Stockholm Univ. (PDF file)).

    87. imp The files can be downloaded from this WWW-page for personal use only!
    I'll appreciate if you will send me an e-mail after downloading files:
    kurasov@math.su.se

    B. Nonrefereed volumes

  87. Three-body Scattering in One Dimension: a Geometric Version of an Adiabatic Approach
    (with Yu.B.Melnikov) In: B.Markovski, S.I.Vinitsky (eds) "Topological Phases in Quantum Theory" ( Proc. Dubna, USSR, 1988), World Scientific, Singapore, 1989.

  88. Cluster Resonances and Bound States and Crystal Band Spectrum
    In: P.Jena, S.N.Khanna, B.K.Rao (eds) "Proc. Int. Symposium on the Physics and Chemistry of Finite Systems: From Clusters to Crystals", Kluwer, Boston-London, 1991.

  89. Nonphysical Sheet and Schroedinger Evolution
    (with B.S.Pavlov) In: "Proc. of the International Workshop "Mathematical Aspects of the Scattering Theory and Applications", Saint-Petersburg, Russia, May 20-24, 1991", St.Petersburg Univ. Press, St.Petersburg, Russia, 1991, p72-81. PDF file

  90. On the Inverse Problem for the Rational Reflection Coefficient
    In: L.Paivarinta, E.Somersalo (eds.) "Inverse Problems in Mathematical Physics", Springer-Verlag, Berlin, 1993, p 126-133. PDF file

  91. Second Virial Coefficient for One-dimensional System
    (with V.Kurasov and B.Pavlov) In: M.Fannes, Ch.Maes, A.Verbeure (eds.) "On Three Levels", Plenum, New York,1994, p 423-428. PDF file

  92. Micro Spectral Properties of Crystals and their Band Structure
    (with B.Pavlov) In: M.Fannes, Ch.Maes, A.Verbeure (eds.) "On Three Levels", Plenum, New York, 1994, p 259-264. PDF file

    imp The files can be downloaded from this WWW-page for personal use only!
    I'll appreciate if you will send me an e-mail after downloading files:
    kurasov@math.su.se

    VI Unpublished preprints

  93. Scattering Theory for Self-Adjoint Extensions
    (with Yu.A.Kuperin, B.S.Pavlov, K.A.Makarov, Yu.B.Melnikov, V.V.Evstratov) Preprint LITH-MAT-R-89-29 Linköping University, Linköping, Sweden, 1989. PDF file

  94. On the Positon Solution of the KdV Equation
    Preprint MSI 93-1, ISSN-1100-214X, Stockholm, Sweden, 1993. PDF file

  95. Scattering on a Lattice in the Stochastic Magnetic Field
    (with A.E.Ryzhkov) Preprint MSI 93-2, ISSN-1100-214X, Stockholm, Sweden, 1993. PDF file

  96. On the delta'-interaction in One Dimension
    (with N.Elander) Preprint MSI 93-7, ISSN-1100-214X, Stockholm, Sweden, 1993. PDF file

  97. Few-body Krein's formula and semibounded from below Schrödinger operator for three quantum particles
    Report N8, Dept. of Math., Stockholm Univ., 1998.

  98. On the reconstruction of the boundary conditions for star graphs
    (with S.Avdonin and M.Nowaczyk) Report 29, Dept. of Math., Lund Univ., 2007. PDF file

  99. On Equi-transmitting Matrices
    (with R. Ogik) Research Report in Mathematics, N1 2014, Dept. of Mathematics, Stockholm Univ. PDF file


  100. On the spectral gap of a quantum graph
    (with J.B. Kennedy, G.Malenova, and D. Mugnolo) Research Report in Mathematics, N5 2015, Dept. of Mathematics, Stockholm Univ. PDF file
  101. Stable Polynomials and crystalline measures
    (with P. Sarnak)  arXiv:2004.05678

imp The files can be downloaded from this WWW-page for personal use only!
I'll appreciate if you will send me an e-mail after downloading files:
kurasov@math.su.se