V. P. Kurdyumov, A. P. Khromov, “Riesz Bases of Eigenfunctions of an Integral Operator with a Variable Limit of Integration”, Mat. Zametki, 76:1 (2004), 97–110; Math. Notes, 76:1 (2004), 90

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Matematicheskie Zametki, 2004, Volume 76, Issue 1, Pages 97–110
DOI: https://doi.org/10.4213/mzm92 (Mi mzm92)

This article is cited in 18 scientific papers (total in 18 papers)

Riesz Bases of Eigenfunctions of an Integral Operator with a Variable Limit of Integration

V. P. Kurdyumov, A. P. Khromov

Saratov State University named after N. G. Chernyshevsky

Full-text PDF (229 kB) Citations (18)

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DOI: https://doi.org/10.4213/mzm92

Abstract: We prove a theorem on the Riesz basis property in the space

L_{2} [0, 1]

$L_2[0,1]$ of the eigenfunctions and associated functions of an integral operator whose kernel possesses a derivative discontinuous on the line

t = 1 - x

$t=1-x$ .

Received: 25.11.2002
Revised: 03.11.2003

English version:
Mathematical Notes, 2004, Volume 76, Issue 1, Pages 90–102
DOI: https://doi.org/10.1023/B:MATN.0000036745.53704.08

Bibliographic databases:

UDC: 517.984

Language: Russian

Citation: V. P. Kurdyumov, A. P. Khromov, “Riesz Bases of Eigenfunctions of an Integral Operator with a Variable Limit of Integration”, Mat. Zametki, 76:1 (2004), 97–110; Math. Notes, 76:1 (2004), 90–102

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm92

https://doi.org/10.4213/mzm92

https://www.mathnet.ru/eng/mzm/v76/i1/p97

This publication is cited in the following 18 articles:

M. Sh. Burlutskaya, “Some properties of functional-differential operators with involution $\nu(x)=1-x$ and their applications”, Russian Math. (Iz. VUZ), 65:5 (2021), 69–76
V. P. Kurdyumov, “O bazisakh Rissa iz sobstvennykh funktsii differentsialnogo operatora vtorogo poryadka s involyutsiei i integralnymi kraevymi usloviyami”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 15:4 (2015), 392–405
V. P. Kurdyumov, A. P. Khromov, “Bazisy Rissa iz sobstvennykh i prisoedinennykh funktsii integralnykh operatorov s razryvnymi yadrami, soderzhaschimi involyutsiyu”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:4(2) (2014), 558–569
V. P. Kurdyumov, A. P. Khromov, “Riesz bases of eigenfunctions of integral operators with kernels discontinuous on the diagonals”, Izv. Math., 76:6 (2012), 1175–1189
M. Sh. Burlutskaya, V. V. Kornev, A. P. Khromov, “Sistema Diraka s nedifferentsiruemym potentsialom i periodicheskimi kraevymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 52:9 (2012), 1621–1632
Kurdyumov V.P. Khromov A.P., “On Riesz Bases of Eigenfunctions of Integral Operators with Kernels Discontinuous on Diagonals”, Dokl. Math., 84:1 (2011), 548–550
V. P. Kurdyumov, A. P. Khromov, “The Riesz bases consisting of eigen and associated functions for a functional differential operator with variable structure”, Russian Math. (Iz. VUZ), 54:2 (2010), 33–45
M. Sh. Burlutskaya, “On Riesz bases of root functions for a class of functional-differential operators on a graph”, Differ. Equ., 45:6 (2009), 779–788
V. P. Kurdyumov, “O bazisakh Rissa iz sobstvennykh funktsii integralnykh operatorov s yadrami, razryvnymi na lomanykh liniyakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:4(1) (2009), 28–35
Djakov P., Mityagin B., “Bari-Markus Property for Riesz Projections of Hill Operators with Singular Potentials”: Meise, R, Functional Analysis and Complex Analysis, Contemporary Mathematics, 481, eds. Aytuna A., Terzioglu T., Vogt D., Amer Mathematical Soc, 2009, 59–80
A. P. Khromov, L. P. Kuvardina, “On the equiconvergence of expansions in eigen- and associated functions of an integral operator with involution”, Russian Math. (Iz. VUZ), 52:5 (2008), 58–66
V. V. Kornev, A. P. Khromov, “Operator integration with an involution in the upper limit of integration”, Dokl. Math., 78:2 (2008), 733–736
V. P. Kurdyumov, A. P. Khromov, “Riesz bases formed by root functions of a functional-differential equation with a reflection operator”, Differ. Equ., 44:2 (2008), 203–212
V. V. Kornev, A. P. Khromov, “Operator integrirovaniya s involyutsiei, imeyuschei stepennuyu osobennost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 8:4 (2008), 18–33
M. Sh. Burlutskaya, A. P. Khromov, “On the equiconvergence of eigenfunction expansions for a first-order functional-differential operator on a cycle-containing graph with two edges”, Differ. Equ., 43:12 (2007), 1638–1647
M. Sh. Burlutskaya, A. P. Khromov, “O skhodimosti srednikh Rissa razlozhenii po sobstvennym funktsiyam funktsionalno-differentsialnogo operatora na grafe-tsikle”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 7:1 (2007), 3–8
V. P. Kurdyumov, A. P. Khromov, “O bazisakh Rissa iz sobstvennykh i prisoedinennykh funktsii funktsionalno-differentsialnogo operatora peremennoi struktury”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 7:2 (2007), 20–25
A. P. Khromov, “Integral operators with kernels that are discontinuous on broken lines”, Sb. Math., 197:11 (2006), 1669–1696

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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