Displaying similar documents to “Laplace integrals in partial differential equations in papers of Bogdan Ziemian”

The modified Cauchy transformation with applications to generalized Taylor expansions

Bogdan Ziemian (1992)

Studia Mathematica

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We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.

Heaviside's theory of signal transmission on submarine cables

Hikosaburo Komatsu (2010)

Banach Center Publications

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As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values,...