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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 3, Pages 591–634 (Mi izv2315)  

This article is cited in 10 scientific papers (total in 10 papers)

Expansion in eigenfunctions of integral operators of convolution on a finite interval with kernels whose Fourier transforms are rational. “Weakly” nonselfadjoint regular kernels

B. V. Pal'tsev


Abstract: A study is made of the asymptotic behavior of the eigenvalues and of expansions in the root vectors of the class of integral operators specified in the title. If some natural conditions, ensuring “regularity” of the asymptotic behavior of the spectrum, are imposed on the kernel, the root vectors form a basis in $L_p(0,T)$ $(1<p<\infty)$ and a Riesz basis in $L_2(0,T)$.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:3, 587–630

Bibliographic databases:

UDC: 517.43
MSC: Primary 45C05, 47G05, 47A70, 45M05; Secondary 46B15
Received: 05.03.1971

Citation: B. V. Pal'tsev, “Expansion in eigenfunctions of integral operators of convolution on a finite interval with kernels whose Fourier transforms are rational. “Weakly” nonselfadjoint regular kernels”, Izv. Akad. Nauk SSSR Ser. Mat., 36:3 (1972), 591–634; Math. USSR-Izv., 6:3 (1972), 587–630

Citation in format AMSBIB
\Bibitem{Pal72}
\by B.~V.~Pal'tsev
\paper Expansion in eigenfunctions of integral operators of convolution on a~finite interval with kernels whose Fourier transforms are rational. ``Weakly'' nonselfadjoint regular kernels
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 3
\pages 591--634
\mathnet{http://mi.mathnet.ru/izv2315}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=303363}
\zmath{https://zbmath.org/?q=an:0237.47026}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 3
\pages 587--630
\crossref{https://doi.org/10.1070/IM1972v006n03ABEH001892}


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

    This publication is cited in the following articles:
    1. Yu. I. Lyubarskii, “Ob operatore svertki na konechnom intervale”, UMN, 31:3(189) (1976), 221–221  mathnet  mathscinet  zmath
    2. Yu. I. Lyubarskii, “On the convolution operator on a finite interval”, Math. USSR-Izv., 11:3 (1977), 583–611  mathnet  crossref  mathscinet  zmath
    3. A. G. Kostyuchenko, A. A. Shkalikov, “Summability of eigenfunction expansions of differential operators and convolution operators”, Funct. Anal. Appl., 12:4 (1978), 262–276  mathnet  crossref  mathscinet  zmath
    4. A. P. Khromov, “Equiconvergence theorems for integrodifferential and integral operators”, Math. USSR-Sb., 42:3 (1982), 331–355  mathnet  crossref  mathscinet  zmath
    5. V. M. Kaplitskii, “An integral equation with matrix difference kernel on an interval”, Sb. Math., 189:8 (1998), 1171–1177  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. B. V. Pal'tsev, “Asymptotic behaviour of the spectra of integral convolution operators on a finite interval with homogeneous polar kernels”, Izv. Math., 67:4 (2003), 695–779  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. P. Kurdyumov, A. P. Khromov, “Riesz Bases of Eigenfunctions of an Integral Operator with a Variable Limit of Integration”, Math. Notes, 76:1 (2004), 90–102  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. M. K. Kerimov, “Boris Vasil'evich Pal'tsev (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 50:7 (2010), 1113–1119  mathnet  crossref  mathscinet  adsnasa  isi  elib
    9. Lev Truskinovsky, Anna Vainchtein, “Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain”, Phys. Rev. E, 90:4 (2014)  crossref
    10. G. M. Gubreev, G. D. Urum, “On a Class of Convolution Operators on a Finite Interval”, Math. Notes, 96:5 (2014), 647–650  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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