Distributions, ultradistributions and other generalized functions
著者
書誌事項
Distributions, ultradistributions and other generalized functions
（Ellis Horwood series in mathematics and its applications）
Ellis Horwood, c1994
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注記
Bibliography: p. [293]-298
Includes index
内容説明・目次
内容説明
This text compares and evaluates various approaches to the theory of distributions which have appeared since the original presentation by Laurent Schwartz in the 1950s. In so doing, it attempts to clarify some of the differences in notation and terminology which have arisen. It includes a systematic treatment of the ultradistributions which arise in connections with the extended definition of the Fourier transform. The authors discuss the problems posed by the definition of "irregular operations" on generalized functions and review solutions proposed by recent researchers. Apart from the introduction of further new classes of generalized functions using standard mathematical methods, the text contains an account of non-standard analysis and its applications to this field.
目次
- Quasi-historical introduction to generalized functions
- classical theories of distributions
- Fourier transforms and ultradistributions
- analytical representation
- other standard theories of generalized functions
- non-standard theories of generalized functions.
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