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Volumn 131, Issue 5, 2003, Pages 1443-1452

On approximations of rank one ℋ-2-perturbations

Author keywords

Self adjoint operators; Singular interactions

Indexed keywords


EID: 0037407145     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06694-7     Document Type: Conference Paper
Times cited : (13)

References (38)
  • 1
    • 0002536193 scopus 로고
    • Zero-radius potentials and M. G. Krein's formula for generalized resolvents
    • Russian, Issled. Linein. Teor. Funktsii. XV
    • V.M.Adarayan and B.S.Pavlov, Zero-radius potentials and M. G. Krein's formula for generalized resolvents, (Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 149 (1986), Issled. Linein. Teor. Funktsii. XV,7-23 (translation in J. Soviet Math., 42 (1988), 1537-1550). MR 87h:47031
    • (1986) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.149 , pp. 7-23
    • Adarayan, V.M.1    Pavlov, B.S.2
  • 2
    • 0013246029 scopus 로고
    • translation in, MR 87h:47031
    • V.M.Adarayan and B.S.Pavlov, Zero-radius potentials and M. G. Krein's formula for generalized resolvents, (Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 149 (1986), Issled. Linein. Teor. Funktsii. XV,7-23 (translation in J. Soviet Math., 42 (1988), 1537-1550). MR 87h:47031
    • (1988) J. Soviet Math. , vol.42 , pp. 1537-1550
  • 5
    • 0033411688 scopus 로고    scopus 로고
    • Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
    • MR 2000g:47011
    • S.Albeverio and V.Koshmanenko, Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions, Potential Anal. 11 (1999), 279-287. MR 2000g:47011
    • (1999) Potential Anal. , vol.11 , pp. 279-287
    • Albeverio, S.1    Koshmanenko, V.2
  • 6
    • 0003126068 scopus 로고    scopus 로고
    • On form-sum approximations of singularly perturbed positive self-adjoint operators
    • MR 2000j:47043
    • S.Albeverio and V.Koshmanenko, On form-sum approximations of singularly perturbed positive self-adjoint operators, J. Func. Anal., 169 (1999), 32-45. MR 2000j:47043
    • (1999) J. Func. Anal. , vol.169 , pp. 32-45
    • Albeverio, S.1    Koshmanenko, V.2
  • 7
    • 0031212486 scopus 로고    scopus 로고
    • Rank one perturbations, approximations and selfadjoint extensions
    • MR 98g:47011
    • S.Albeverio and P.Kurasov, Rank one perturbations, approximations and selfadjoint extensions. J. Func. Anal., 148 (1997), 152-169. MR 98g:47011
    • (1997) J. Func. Anal. , vol.148 , pp. 152-169
    • Albeverio, S.1    Kurasov, P.2
  • 8
    • 0031460635 scopus 로고    scopus 로고
    • Rank one perturbations of not semibounded operators
    • MR 98k:47025
    • S.Albeverio and P.Kurasov, Rank one perturbations of not semibounded operators, Integr. Equ. Oper. Theory, 27 (1997), 379-400. MR 98k:47025
    • (1997) Integr. Equ. Oper. Theory , vol.27 , pp. 379-400
    • Albeverio, S.1    Kurasov, P.2
  • 9
    • 22644450942 scopus 로고    scopus 로고
    • Finite rank perturbations and distribution theory
    • MR 99m:47012
    • S.Albeverio and P.Kurasov, Finite rank perturbations and distribution theory, Proc. Amer. Math. Soc., 127 (1999), 1151-1161. MR 99m:47012
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 1151-1161
    • Albeverio, S.1    Kurasov, P.2
  • 10
    • 0013237130 scopus 로고    scopus 로고
    • Singular perturbations of differential operators. Solvable Schrödinger type operators
    • Cambridge University Press, Cambridge, MR 2001g:47084
    • S.Albeverio and P.Kurasov, Singular perturbations of differential operators. Solvable Schrödinger type operators, London Mathematical Society Lecture Note Series, 271, Cambridge University Press, Cambridge, 2000, xiv+429 pp. MR 2001g:47084
    • (2000) London Mathematical Society Lecture Note Series , vol.271
    • Albeverio, S.1    Kurasov, P.2
  • 11
    • 0013290322 scopus 로고    scopus 로고
    • Approximation of general zero-range potentials
    • MR 2002c:81035
    • S.Albeverio and L.Nizhnik, Approximation of general zero-range potentials, Ukrainian Math. J., 5 (2000). MR 2002c:81035
    • (2000) Ukrainian Math. J. , vol.5
    • Albeverio, S.1    Nizhnik, L.2
  • 12
    • 0002781662 scopus 로고
    • The Birman-Kreǐn-Vishik theory of selfadjoint extensions of semi-bounded operators
    • MR 81m:47038
    • A.Alonso and B.Simon, The Birman-Kreǐn-Vishik theory of selfadjoint extensions of semi-bounded operators, J. Operator Theory, 4 (1980), 251-270. MR 81m:47038
    • (1980) J. Operator Theory , vol.4 , pp. 251-270
    • Alonso, A.1    Simon, B.2
  • 13
    • 0000447975 scopus 로고
    • A remark on Schrödinger equation with a singular potential
    • MR 23:B2345
    • F.A.Berezin and L.D.Faddeev, A remark on Schrödinger equation with a singular potential, Soviet Math. Dokl., 137 (1961), 1011-1014. MR 23:B2345
    • (1961) Soviet Math. Dokl. , vol.137 , pp. 1011-1014
    • Berezin, F.A.1    Faddeev, L.D.2
  • 14
    • 22044453335 scopus 로고    scopus 로고
    • Finite rank singular perturbations and distributions with discontinuous test functions
    • MR 98g:47012
    • J.Boman and P.Kurasov, Finite rank singular perturbations and distributions with discontinuous test functions, Proc. Amer. Math. Soc., 126 (1998), 1673-1683. MR 98g:47012
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 1673-1683
    • Boman, J.1    Kurasov, P.2
  • 16
    • 0001761938 scopus 로고
    • Scattering from generalized point interactions using selfadjoint extensions in Pontryagin spaces
    • MR 92e:81028
    • J.F.van Diejen and A.Tip, Scattering from generalized point interactions using selfadjoint extensions in Pontryagin spaces, J. Math. Phys., 32 (1991), 630-641. MR 92e:81028
    • (1991) J. Math. Phys. , vol.32 , pp. 630-641
    • Van Diejen, J.F.1    Tip, A.2
  • 17
    • 0001412433 scopus 로고    scopus 로고
    • Self-adjoint operators with inner singularities and Pontryagin spaces, Operator theory and related topics
    • Vol. II (Odessa), Birkhäuser, Basel, MR 2001f:47039
    • 16. A.Dijksma, H.Langer, Yu.Shondin, and C. Zeinstra, Self-adjoint operators with inner singularities and Pontryagin spaces, Operator theory and related topics, Vol. II (Odessa, 1997), 105-175, Oper. Theory Adv. Appl., 118, Birkhäuser, Basel, 2000. MR 2001f:47039
    • (1997) Oper. Theory Adv. Appl. , vol.118 , pp. 105-175
    • Dijksma, A.1    Langer, H.2    Shondin, Yu.3    Zeinstra, C.4
  • 18
    • 0001323468 scopus 로고
    • Rank-one perturbations at infinite coupling
    • MR 95m:47014
    • F.Gesztesy and B.Simon, Rank-one perturbations at infinite coupling, J. Func. Anal., 128 (1995), 245-252. MR 95m:47014
    • (1995) J. Func. Anal. , vol.128 , pp. 245-252
    • Gesztesy, F.1    Simon, B.2
  • 19
    • 0031475005 scopus 로고    scopus 로고
    • On rank one perturbations of selfadjoint operators
    • MR 98k:47027
    • S.Hassi and H.de Snoo, On rank one perturbations of selfadjoint operators, Integral Equations Operator Theory, 29 (1997), 288-300. MR 98k:47027
    • (1997) Integral Equations Operator Theory , vol.29 , pp. 288-300
    • Hassi, S.1    De Snoo, H.2
  • 20
    • 22044449100 scopus 로고    scopus 로고
    • Smooth rank one perturbations of selfadjoint operators
    • MR 98k:47028
    • S.Hassi, H.de Snoo, and A.Willemsma, Smooth rank one perturbations of selfadjoint operators, Proc. Amer. Math. Soc., 126 (1998), 2663-2675. MR 98k:47028
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 2663-2675
    • Hassi, S.1    De Snoo, H.2    Willemsma, A.3
  • 21
    • 0001440491 scopus 로고
    • Rank one perturbations with infinitesimal coupling
    • MR 96e:47012
    • A.Kiselev and B.Simon, Rank one perturbations with infinitesimal coupling, J. Func. Anal., 130 (1995), 345-356. MR 96e:47012
    • (1995) J. Func. Anal. , vol.130 , pp. 345-356
    • Kiselev, A.1    Simon, B.2
  • 22
    • 0001300777 scopus 로고
    • Towards the rank-one singular perturbations of self-adjoint operators
    • V. Koshmanenko, Towards the rank-one singular perturbations of self-adjoint operators, Ukrainian Math. J., 43 (1991), 1559-1566.
    • (1991) Ukrainian Math. J. , vol.43 , pp. 1559-1566
    • Koshmanenko, V.1
  • 24
    • 0000447568 scopus 로고
    • On Hermitian operators whose deficiency indices are 1
    • MR 6:131a
    • M.G.Krein, On Hermitian operators whose deficiency indices are 1, C. R, (Doklady) Acad. Sci URSS (N.S.), 43 (1944), 323-326. MR 6:131a
    • (1944) C. R. (Doklady) Acad. Sci URSS (N.S.) , vol.43 , pp. 323-326
    • Krein, M.G.1
  • 25
    • 0000447567 scopus 로고
    • On Hermitian operators whose deficiency indices equal to one. II
    • MR 6:179a
    • M.G.Krein, On Hermitian operators whose deficiency indices equal to one. II, C. R. (Doklady) Acad. Sci URSS (N.S.), 44 (1944), 131-134. MR 6:179a
    • (1944) C. R. (Doklady) Acad. Sci URSS (N.S.) , vol.44 , pp. 131-134
    • Krein, M.G.1
  • 26
    • 0030187273 scopus 로고    scopus 로고
    • Distribution theory for discontinuous test functions and differential operators with generalized coefficients
    • MR 97g:46050
    • P.Kurasov. Distribution theory for discontinuous test functions and differential operators with generalized coefficients, J. Math. Anal. Appl., 201 (1996), 297-323. MR 97g:46050
    • (1996) J. Math. Anal. Appl. , vol.201 , pp. 297-323
    • Kurasov, P.1
  • 27
    • 0013188605 scopus 로고    scopus 로고
    • -n-perturbations of self-adjoint operator and Krein's resolvent formula
    • Research Report N4, Stockholm Univ.
    • -n-perturbations of self-adjoint operator and Krein's resolvent formula, Research Report N4, Stockholm Univ., 2001; accepted for publication in Integr. Eq. Oper. Theory.
    • (2001) Integr. Eq. Oper. Theory
    • Kurasov, P.1
  • 28
    • 0013295847 scopus 로고    scopus 로고
    • -3-perturbations of positive self-adjoint operators. Stochastic processes, physics and geometry: New interplays, II
    • Leipzig, Amer. Math. Soc., Providence, RI, MR 2001j:47012
    • -3-perturbations of positive self-adjoint operators. Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), 413-422, CMS Conf. Proc., 29. Amer. Math. Soc., Providence, RI, 2000. MR 2001j:47012
    • (1999) CMS Conf. Proc. , vol.29 , pp. 413-422
    • Kurasov, P.1    Watanabe, K.2
  • 30
    • 0002069185 scopus 로고    scopus 로고
    • -2-construction and some applications
    • Mathematical results in quantum mechanics (Prague), Birkhäuser, Basel, MR 2000f:47022
    • -2-construction and some applications, Mathematical results in quantum mechanics (Prague, 1998), 99-105, Oper. Theory Adv. Appl., 108, Birkhäuser, Basel, 1999. MR 2000f:47022
    • (1998) Oper. Theory Adv. Appl. , vol.108 , pp. 99-105
    • Kuroda, S.T.1    Nagatani, H.2
  • 31
    • 0013251653 scopus 로고    scopus 로고
    • On point interactions in quantum mechanics
    • L.Nizhnik. On point interactions in quantum mechanics, Ukrainian Math. J., 49 (1997), 1557-1560.
    • (1997) Ukrainian Math. J. , vol.49 , pp. 1557-1560
    • Nizhnik, L.1
  • 32
    • 0002039451 scopus 로고
    • The theory of extensions, and explicitly solvable models
    • Russian, MR 89b:47009
    • B.S.Pavlov, The theory of extensions, and explicitly solvable models. (Russian), Uspekhi Mat. Nauk, 42 (1987), 99-131. MR 89b:47009
    • (1987) Uspekhi Mat. Nauk , vol.42 , pp. 99-131
    • Pavlov, B.S.1
  • 33
    • 0000818311 scopus 로고
    • Boundary conditions on thin manifolds and the semiboundedness of the three-body Schrödinger operator with point potential
    • Russian
    • B.S.Pavlov, Boundary conditions on thin manifolds and the semiboundedness of the three-body Schrödinger operator with point potential, (Russian), Mat. Sb. (N.S.), 136(178) (1988), 163-177 (translation in Math. USSR-Sb., 64 (1989), 161-175). MR 90g:35120
    • (1988) Mat. Sb. (N.S.) , vol.136 , Issue.178 , pp. 163-177
    • Pavlov, B.S.1
  • 34
    • 0000296262 scopus 로고
    • translation in, MR 90g:35120
    • B.S.Pavlov, Boundary conditions on thin manifolds and the semiboundedness of the three-body Schrödinger operator with point potential, (Russian), Mat. Sb. (N.S.), 136(178) (1988), 163-177 (translation in Math. USSR-Sb., 64 (1989), 161-175). MR 90g:35120
    • (1989) Math. USSR-Sb. , vol.64 , pp. 161-175
  • 35
    • 0000267562 scopus 로고
    • n connected with extensions of the energy operator in a Pontryagin space
    • Russian, translation in Theoret. and Math. Phys., 74 (1988), 220-230. MR 89f:81042
    • n connected with extensions of the energy operator in a Pontryagin space, (Russian) Teoret. Mat. Fix., 74 (1988), 331-344 (translation in Theoret. and Math. Phys., 74 (1988), 220-230). MR 89f:81042
    • (1988) Teoret. Mat. Fix. , vol.74 , pp. 331-344
    • Shondin, Yu.1
  • 36
    • 0013182928 scopus 로고
    • Perturbation of elliptic operators on thin sets of high codimension, and extension theory in a space with an indefinite metric
    • Russian, Issled, po Linein. Oper, i Teor. Funktsii. 23
    • Yu.Shondin, Perturbation of elliptic operators on thin sets of high codimension, and extension theory in a space with an indefinite metric, (Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 222 (1995), Issled, po Linein. Oper, i Teor. Funktsii. 23, 246-292 (translation in J. Math. Sci. (New York) 87 (1997), 3941-3970). MR 97e:47084
    • (1995) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) , vol.222 , pp. 246-292
    • Shondin, Yu.1
  • 37
    • 0013290323 scopus 로고    scopus 로고
    • translation in, MR 97e:47084
    • Yu.Shondin, Perturbation of elliptic operators on thin sets of high codimension, and extension theory in a space with an indefinite metric, (Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 222 (1995), Issled, po Linein. Oper, i Teor. Funktsii. 23, 246-292 (translation in J. Math. Sci. (New York) 87 (1997), 3941-3970). MR 97e:47084
    • (1997) J. Math. Sci. (New York) , vol.87 , pp. 3941-3970
  • 38
    • 0001758451 scopus 로고
    • Spectral analysis of rank one perturbations and applications
    • MR 97c:47008
    • B.Simon, Spectral analysis of rank one perturbations and applications, in "CRM Proceedings and Lecture Notes", 8 (1995), 109-149. MR 97c:47008
    • (1995) CRM Proceedings and Lecture Notes , vol.8 , pp. 109-149
    • Simon, B.1


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