Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Symmetrization of distributions and its application. II. Liouville type problem in convolution equations
HTML articles powered by AMS MathViewer

by Kuang-ho Chen PDF
Trans. Amer. Math. Soc. 171 (1972), 179-194 Request permission

Abstract:

The symmetrization of distributions corresponding to a bounded $n - 1$ dimensional ${C^\infty }$-submanifold of a ${C^\infty }$-manifold is constructed. This device reduces the consideration of distributions in ${R^n}$ to the one of distributions in ${R^1}$, i.e. the symmetrized distributions. Using the relation between the inverse Fourier transform of a symmetrized distribution and the one of the original (nonsymmetrized) distribution, we determine the rate of decay at infinity of solutions to a general convolution equation necessary to assure uniqueness. Using a result in the division problem for distributions, we achieve the following result: If $u \in C({R^n})$ is a solution of the convolution equation $S \ast u = f,f \in \mathcal {D}({R^n})$, with some suitable $S \in \mathcal {E}’({R^n})$, then $u \in \mathcal {D}({R^n})$, provided $u$ decays sufficiently fast at infinity.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46F10, 35G05, 47B99
  • Retrieve articles in all journals with MSC: 46F10, 35G05, 47B99
Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 171 (1972), 179-194
  • MSC: Primary 46F10; Secondary 35G05, 47B99
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0630201-6
  • MathSciNet review: 0630201