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

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

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
2. V. G. Kurbatov, “Algebras of difference and integral operators”, Funct. Anal. Appl., 24:2 (1990), 156–158
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
4. A. G. Baskakov, “On Spectral Properties of Some Classes of Linear Operators”, Funct. Anal. Appl., 29:2 (1995), 121–123
5. R. Grigorchuk, P. Harpe, “On problems related to growth, entropy, and spectrum in group theory”, J Dyn Control Syst, 3:1 (1997), 51
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
7. J. Brüning, V. A. Geiler, “Gauge-periodic point perturbations on the Lobachevsky plane”, Theoret. and Math. Phys., 119:3 (1999), 687–697
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
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
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
11. V. S. Rabinovich, S. Roch, “Essential Spectrum of Difference Operators on Periodic Metric Spaces”, Funct. Anal. Appl., 43:2 (2009), 151–154
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
13. Theory Probab. Appl., 56:1 (2012), 1–20
14. E. B. Yarovaya, “Spectral Properties of Evolutionary Operators in Branching Random Walk Models”, Math. Notes, 92:1 (2012), 115–131
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
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