Skip to content

Advertisement

Advances in Difference Equations
Advances in Difference Equations Cover Image
  • Research Article
  • Open Access

On difference equation with generalized dilation

Advances in Difference Equations20062006:027512

https://doi.org/10.1155/ADE/2006/27512

©  Pavel Plaschinsky. 2006

  • Received: 22 July 2004
  • Accepted: 27 January 2005
  • Published:

Abstract

We investigate the functional equation with generalized dilation in the special weighted functional spaces. We provide some sufficient conditions for the existence of the inversion operator in the same form and consider several examples.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

[12345678]

Authors’ Affiliations

(1)
Faculty of Mathematics and Mechanics, Belarusian State University, Skaryny Avenue 4F, Minsk, 220050, Belarus

References

  1. Antonevich A, Belousov M, Lebedev A: Functional Differential Equations. II. C∗-Applications. Part 2. Equations with Discontinuous Coefficients and Boundary Value Problems, Pitman Monographs and Surveys in Pure and Applied Mathematics. Volume 95. Longman, Harlow; 1998:x+414.Google Scholar
  2. Antonevich A, Belousov M, Lebedev A: Functional Differential Equations. II. C∗-Applications. Part 1. Equations with Continuous Coefficients, Pitman Monographs and Surveys in Pure and Applied Mathematics. Volume 94. Longman, Harlow; 1998:x+384.Google Scholar
  3. Antonevich A, Lebedev A: Functional-Differential Equations. I. C∗-Theory, Pitman Monographs and Surveys in Pure and Applied Mathematics. Volume 70. Longman Scientific & Technical, Harlow; 1994:viii+504.Google Scholar
  4. Chen NX: Modified Möbius inverse formula and its applications in physics. Physical Review Letters 1990,64(11):1193–1195. 10.1103/PhysRevLett.64.1193MathSciNetView ArticleMATHGoogle Scholar
  5. Estrada R: Dirichlet convolution inverses and solution of integral equations. Journal of Integral Equations and Applications 1995,7(2):159–166. 10.1216/jiea/1181075867MathSciNetView ArticleMATHGoogle Scholar
  6. Plaschinsky PV: Discrete Mellin convolution with dilation and its applications. Mathematical Modelling and Analysis 1998, 3: 160–167.MathSciNetMATHGoogle Scholar
  7. Plaschinsky PV: One functional operator inversion formula. Mathematical Modelling and Analysis 2001,6(1):138–146.MathSciNetMATHGoogle Scholar
  8. Przeworska-Rolewicz D: Equations with Transformed Argument. An Algebraic Approach. Elsevier Scientific Publishing, Amsterdam; PWN—Polish Scientific, Warsaw; 1973:xv+354.MATHGoogle Scholar

Copyright

© Pavel Plaschinsky. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advertisement