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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 3, Pages 652–671 (Mi izv1369)  

This article is cited in 15 scientific papers (total in 15 papers)

Pseudodifference operators and their Green's functions

M. A. Shubin


Abstract: The author studies pseudodifference operators on a discrete metric space, where the matrix elements of the operators decrease faster than a system of singular functions of the distance between points determining a matrix element. Similar estimates for matrix elements are proved for the inverse of a pseudodifference operator in the case where the weight functions increase faster than any function of the volume (the number of points in the ball of radius $r$ with prescribed center) and slower than the standard exponential function.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:3, 605–622

Bibliographic databases:

UDC: 517.43
MSC: Primary 47B39, 47B37; Secondary 47B38
Received: 03.06.1983

Citation: M. A. Shubin, “Pseudodifference operators and their Green's functions”, Izv. Akad. Nauk SSSR Ser. Mat., 49:3 (1985), 652–671; Math. USSR-Izv., 26:3 (1986), 605–622

Citation in format AMSBIB
\Bibitem{Shu85}
\by M.~A.~Shubin
\paper Pseudodifference operators and their Green's functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 3
\pages 652--671
\mathnet{http://mi.mathnet.ru/izv1369}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=794959}
\zmath{https://zbmath.org/?q=an:0595.39008|0574.39006}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 3
\pages 605--622
\crossref{https://doi.org/10.1070/IM1986v026n03ABEH001161}


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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. V. G. Kurbatov, “On the invertibility of almost periodic operators”, Math. USSR-Sb., 67:2 (1990), 367–377  mathnet  crossref  mathscinet  zmath  isi
    2. V. G. Kurbatov, “Algebras of difference and integral operators”, Funct. Anal. Appl., 24:2 (1990), 156–158  mathnet  crossref  mathscinet  zmath  isi
    3. A. G. Baskakov, “Wiener's theorem and the asymptotic estimates of the elements of inverse matrices”, Funct. Anal. Appl., 24:3 (1990), 222–224  mathnet  crossref  mathscinet  zmath  isi
    4. A. G. Baskakov, “On Spectral Properties of Some Classes of Linear Operators”, Funct. Anal. Appl., 29:2 (1995), 121–123  mathnet  crossref  mathscinet  zmath  isi
    5. R. Grigorchuk, P. Harpe, “On problems related to growth, entropy, and spectrum in group theory”, J Dyn Control Syst, 3:1 (1997), 51  crossref  mathscinet  zmath  elib
    6. A. G. Baskakov, “Estimates for the entries of inverse matrices and the spectral analysis of linear operators”, Izv. Math., 61:6 (1997), 1113–1135  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. J. Brüning, V. A. Geiler, “Gauge-periodic point perturbations on the Lobachevsky plane”, Theoret. and Math. Phys., 119:3 (1999), 687–697  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. T. V. Azarnova, I. A. Kolesnikov, “Otsenki elementov obratnykh matrits dlya operatorov s lentochnymi matritsami”, Sib. zhurn. vychisl. matem., 3:4 (2000), 323–331  mathnet  zmath
    9. T. V. Azarnova, “Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure”, Math. Notes, 72:1 (2002), 3–9  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Karlovich Yu.I., “Nonlocal singular integral operators with slowly oscillating data”, Operator Algebras, Operator Theory and Applications, Operator Theory : Advances and Applications, 181, 2008, 229–261  isi
    11. V. S. Rabinovich, S. Roch, “Essential Spectrum of Difference Operators on Periodic Metric Spaces”, Funct. Anal. Appl., 43:2 (2009), 151–154  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. E. B. Yarovaya, “Criterions of the exponential growth of particles for some models of branching random walks”, Theory Probab. Appl., 55:4 (2011), 661–682  mathnet  crossref  crossref  mathscinet  isi
    13. Theory Probab. Appl., 56:1 (2012), 1–20  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. E. B. Yarovaya, “Spectral Properties of Evolutionary Operators in Branching Random Walk Models”, Math. Notes, 92:1 (2012), 115–131  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. Garkavenko G.V. Uskova N.B., “Method of Similar Operators in Research of Spectral Properties of Difference Operators With Growthing Potential”, Sib. Electron. Math. Rep., 14 (2017), 673–689  mathnet  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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