On some contributions of John Horváth to the theory of distributions. (English) Zbl 1063.46027
This paper is an exposition of some contributions of Professor J. Horváth to the theory of distributions. The first section is concerned with the nature of singular integrals and special emphasis is placed on the study of the Riesz kernels. The second section deals with analytic continuation of distribution-valued functions. Applications to the derivation of the fundamental solution of some differential operators are included, as well as the connection with Hadamard’s finite parts. The search for a definition of convolution as general and symmetric as possible is the content of the final section. As an application of the general convolution, the author presents a composition formula for elliptic Riesz kernels.
Reviewer: Antonio Galbis (Valencia)
MSC:
| 46F10 | Operations with distributions and generalized functions |
| 01A60 | History of mathematics in the 20th century |
| 46N20 | Applications of functional analysis to differential and integral equations |
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