Hermite transform for distribution and Boehmian space
Abstract
Hermite transform involves weigth function and Hermite polynomial as its kernel is discussed. The Hermite transform and its basic properties are extended to the distribution spaces and to the space of integrable Boehmian
Downloads
References
P. K. Banerji, Unfolding the concept of Boehmians and their applications, Math. Student 75 (1-4) (2006), 87-121.
P. K. Banerji, Deshna Loonker and S. L. Kalla, Kontorovich - Lebedev transform for Boehmians, Integral Trans. Spl. Funct. 20 (12) (2009), 905-913. DOI: https://doi.org/10.1080/10652460902987060
L. Debnath, On Hermite Transforms, Math. Vesnik, 1 (16) (1964), 285-292.
L. Debnath, Some operational properties of the Hermite transform, Math. Vesnik, 5 (20) (1968), 29-36
Lokenath Debnath and Dambaru Bhatta, Integral Transforms and their Applications, Chapman and Hall/CRC, Taylor and Francis Group, Boca Raton, London (2007).
I. H. Dimovski. and S. L. Kalla, Explicit convolution for Hermite transform, Math. Japonica 33 (1988), 345-351.
H. J. Glaeske, On a convolution structure of a generalized Hermite transformation, Serdica 9 (1983), 223-229.
H. J.Glaeske, Convolution structure of (generalized) Hermite transforms, Algebraic Analysis & related topics, Banach Centre Publ. 53 (2000), 113-120.
H. J. Glaeske, A. P. Prudnikov and K. A. Skornik, Operational Calculus and Related Topics, Champan & Hall/CRC, Boca Raton, New York (2006). DOI: https://doi.org/10.1201/9781420011494
Deshna Loonker, P. K. Banerji.and Lokenath Debnath, Hartley transform for integrable Boehmians, Integral Trans. Spl. Funct. 21 (6) (2010), 459-464. DOI: https://doi.org/10.1080/10652460903360903
C. Markett, The product formula and convolution structure associated with generalizd Hermite polynomails, J. Approx. Theory 73 (1993), 199-217. DOI: https://doi.org/10.1006/jath.1993.1038
J. Mikusinski and P. Mikusinski, Quotients de suites et leurs applications dans l’ analyse fonctionnlle. C. R. Acad. Sc. Paris, 293, Ser. I (1981), 463-464.
P. Mikusinski, Convergence of Boehmians, Japan J. Math. 9 (1) (1983), 159-179. DOI: https://doi.org/10.4099/math1924.9.159
P. Mikusinski, Boehmians and Generalized Functions, Acata Math. Hung. 51 (3-4) (1988), 271-281. DOI: https://doi.org/10.1007/BF01903334
A. H. Zemanian, Distribution Theory and Transform Analysis, McGraw Hill Book Co., New York, San Francisco (1965).
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
