The Weierstrass Transform for a Class of Generalized Functions

✍ Scribed by V Karunakaran; T Venugopal

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 251 KB
• Volume: 220
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5836

✦ Synopsis

The classical theory of the Weierstrass transform is extended to a generalized function space which is the dual of a testing function space consisting of purely entire functions with certain growth conditions developed by Kenneth B. Howell. An inversion formula and characterizations for this transform are obtained. A comparative study with the existing literature is also undertaken.