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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 4, Pages 59–74 (Mi izv647)  

This article is cited in 6 scientific papers (total in 6 papers)

Absolute convergence of expansions in eigen- and adjoint functions of an integral operator with a variable limit of integration

V. V. Kornev, A. P. Khromov


Abstract: We establish an analogue of Zygmund's criterion for the absolute convergence of trigonometric Fourier series for expansions in eigen- and adjoint functions of the integral operator $Af(x)=\int_0^{1-x}A(1-x,t)f(t) dt$.

DOI: https://doi.org/10.4213/im647

Full text: PDF file (939 kB)
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English version:
Izvestiya: Mathematics, 2005, 69:4, 703–717

Bibliographic databases:

UDC: 517.968
MSC: 47G10, 45P05, 42A20
Received: 05.03.2004

Citation: V. V. Kornev, A. P. Khromov, “Absolute convergence of expansions in eigen- and adjoint functions of an integral operator with a variable limit of integration”, Izv. RAN. Ser. Mat., 69:4 (2005), 59–74; Izv. Math., 69:4 (2005), 703–717

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Khromov, “Integral operators with kernels that are discontinuous on broken lines”, Sb. Math., 197:11 (2006), 1669–1696  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. V. Kornev, “Absolute and Uniform Convergence of Eigenfunction Expansions of Integral Operators with Kernels Admitting Derivative Discontinuities on the Diagonals”, Math. Notes, 81:5 (2007), 638–648  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Khromov A.I., Kocherov E.P., Grigor'eva A.L., “Strain states and fracture conditions for rigid-plastic bodies”, Dokl. Phys., 52:4 (2007), 228–232  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    4. 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  mathnet
    5. 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  mathnet  crossref  mathscinet  zmath  elib
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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