Fundamental solutions for differential equations associated with the number operator

Author:
Yuh Jia Lee

Journal:
Trans. Amer. Math. Soc. **268** (1981), 467-476

MSC:
Primary 35R15; Secondary 28C20, 46G99, 58D20, 60J99

DOI:
https://doi.org/10.1090/S0002-9947-1981-0632538-9

Correction:
Trans. Amer. Math. Soc. **276** (1983), 621-624.

MathSciNet review:
632538

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an abstract Wiener space. If is a twice -differentiable function on such that and is of trace class, then we define , where is the Laplacian and denotes the - pairing. The closure of is known as the number operator. In this paper, we investigate the existence, uniqueness and regularity of solutions for the following two types of equations: (1) (initial value problem) and (2) . We show that the fundamental solutions of (1) and (2) exist in the sense of measures and we represent their solutions by integrals with respect to these measures.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0632538-9

Keywords:
Abstract Wiener space,
Wiener measure,
-differentiation,
number operator,
fundamental solution

Article copyright:
© Copyright 1981
American Mathematical Society