Opuscula Math. 36, no. 4 (2016), 525-539

Opuscula Mathematica

On solvability of some difference-discrete equations

Alexander V. Vasilyev
Vladimir B. Vasilyev

Abstract. 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.

Keywords: multidimensional difference-discrete equation, symbol, factorization, periodic Riemann problem.

Mathematics Subject Classification: 39A14, 42B05.

Full text (pdf)

  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, Birkhäuser, 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. Prössdorf, 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; Birkhäuser, 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.
  • Alexander V. Vasilyev
  • National Research Belgorod State University, Department of Mathematical Analysis, Studencheskaya 14/1, Belgorod 307008, Russia
  • Vladimir B. Vasilyev
  • Chair of Pure Mathematics, Lipetsk State Technical University, Lipetsk 398600, Russia
  • Communicated by Josef Diblík.
  • Received: 2015-09-17.
  • Accepted: 2016-01-26.
  • Published online: 2016-04-01.
Opuscula Mathematica - cover

Cite this article as:
Alexander V. Vasilyev, Vladimir B. Vasilyev, On solvability of some difference-discrete equations, Opuscula Math. 36, no. 4 (2016), 525-539, http://dx.doi.org/10.7494/OpMath.2016.36.4.525

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.