Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Hankel transforms and GASP

Author: Stanton Philipp
Journal: Trans. Amer. Math. Soc. 176 (1973), 59-72
MSC: Primary 44A15
MathSciNet review: 0316978
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The inversion of the classical Hankel transform is considered from three viewpoints. The first approach is direct, and a theorem is given which allows inversion in the (C, 1) sense under fairly weak hypotheses. The second approach is via Abel summability, and it is shown that inversion is possible if it is known that the Hankel transform is Abel summable and if certain critical growth conditions are satisfied. The third approach rests on the observation that Abel means of Hankel transforms satisfy a variant of the GASP equation in two arguments. In this setting the inversion problem becomes a boundary value problem for GASP in a quadrant of the plane with boundary values on one of the axes; a uniqueness theorem for this problem is proved which is best possible in several respects.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 44A15

Retrieve articles in all journals with MSC: 44A15

Additional Information

PII: S 0002-9947(1973)0316978-9
Keywords: Hankel transform, GASP, locally integrable, kernel, inversion, smooth, generalized second derivative, Bessel function, Legendre function of second kind, hypergeometric function, binomial coefficient
Article copyright: © Copyright 1973 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia