Hermite transform
From Encyclopedia of Mathematics
The integral
where are the Hermite polynomials. The inversion formula is
provided that the series converges. The Hermite transform reduces the operator
to an algebraic one by the formula
If and all its derivatives up to and including the -th order are bounded, then
The Hermite transform has also been introduced for a special class of generalized functions (see [2]). They are used to solve differential equations containing the operator .
References
[1] | L. Debnath, "On the Hermite transform" Mat. Vesnik , 1 (1964) pp. 285–292 |
[2] | A.G. Zemanian, "Generalized integral transforms" , Wiley (1968) |
How to Cite This Entry:
Hermite transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hermite_transform&oldid=13762
Hermite transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hermite_transform&oldid=13762
This article was adapted from an original article by Yu.A. BrychkovA.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article