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On solvability of some difference-discrete equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Multidimensional difference equations in a discrete half-space are considered. Using the theory of periodic Riemann problems a general solution and solvability conditions in discrete Lebesgue spaces are obtained. Some statements of boundary value problems of discrete type are given.
Rocznik
Strony
525--539
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • National Research Belgorod State University Department of Mathematical Analysis Studencheskaya 14/1, Belgorod 307008, Russia
  • Chair of Pure Mathematics Lipetsk State Technical University Lipetsk 398600, Russia
Bibliografia
  • [1] D.E. Dudgeon, R.M. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, 1984.
  • [2] G. Eskin, Boundary Value Problems for Elliptic Pseudodifferential Equations, AMS, Providence, 1981.
  • [3] F.D. Gakhov, Boundary Value Problems, Dover Publications, NY, 1981.
  • [4] I. Gokhberg, N. Krupnik, Introduction to the Theory of One Dimensional Singular-Integral Equations, Birkhauser, Basel, 2010.
  • [5] C. Jordan, Calculus of Finite Differences, Chelsea Publishing Company, New York, NY, 1950.
  • [6] V.G. Kurbatov, Functional Differential Operators and Equations, Kluwer Academic Publishers, Dordrecht, 1999.
  • [7] S.G. Mikhlin, S. Próssdorf, Singular Integral Operators, Berlin, Akademie-Verlag, 1986.
  • [8] L.M. Milne-Thomson, The Calculus of Finite Differences, Chelsea Publishing Company, New York, NY, 1981.
  • [9] N.I. Muskhelishvili, Singular Integral Equations, North Holland, 1976.
  • [10] B. Noble, Methods Based on Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, London-New York-Paris-Los Angeles, 1958.
  • [11] S.L. Sobolev, Cubature Formulas and Modern Analysis: An Introduction, Gordon and Breach Sci. Publ., Montreux, 1992.
  • [12] E. Titchmarsh, Introduction to the Theory of Fourier Integrals, Chelsea Publishing Company, New York, NY, 1986.
  • [13] V.B. Vasil'ev, Wave Factorization of Elliptic Symbols: Theory and Applications. Introduction to the Theory of Boundary Value Problems in Non-Smooth Domains, Dordrecht-Boston-London, Kluwer Academic Publishers, 2000.
  • [14] V.B. Vasilyev, General boundary value problems for pseudo differential equations and related difference equations, Adv. Difference Equ. (2013) 2013:289.
  • [15] V.B. Vasilyev, On some difference equations of first order, Tatra Mt. Math. Publ. 54 (2013), 165-181.
  • [16] A.V. Vasilyev, V.B. Vasilyev, Discrete singular operators and equations in a half-space, Azerb. J. Math. 3 (2013) 1, 84-93.
  • [17] A.V. Vasilyev, V.B. Vasilyev, Discrete singular integrals in a half-space, [in:] Current Trends in Analysis and Its Applications, Proc. 9th ISAAC Congress, Krakow, Poland, 2013; Birkhauser, Basel, 2015, 663-670.
  • [18] A.V. Vasilyev, V.B. Vasilyev, Periodic Riemann problem and discrete convolution equations, Differ. Equ. 51 (2015) 5, 652-660.
  • [19] A.V. Vasilyev, V.B. Vasilyev, On some classes of difference equations of infinite order, Adv. Difference Equ. (2015) 2015:211.
  • [20] V.S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables, Dover Publications, NY, 2007.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-acd76275-1fa1-4393-8231-c8f2c95489ee
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