Hermite transform
From Encyclopedia of Mathematics
The integral
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where are the Hermite polynomials. The inversion formula is
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provided that the series converges. The Hermite transform reduces the operator
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to an algebraic one by the formula
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If and all its derivatives up to and including the
-th order are bounded, then
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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=47217
Hermite transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hermite_transform&oldid=47217
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