Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis

Dong Myung Chung and Un Cig Ji
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Dong Myung Chung: Sogang University, Department of Mathematics
Un Cig Ji: Seoul National University, Global Analysis Research Center, Department of Mathematics

A chapter in Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, 2001, pp 89-100 from Springer

Abstract: Abstract In this paper we shall show the heredity of a differentiable one-parameter semigroup under the second quantization and then discuss the resolvent of the differential second quantization operator and the potentials of test white noise functionals. As an application, we shall investigate the existence of solutions of the Poisson-type equations associated with differential second quantization operators as well as operators similar to differential second quantization operators.

Keywords: 60H40; 46F25; 47D06; white noise; differential second quantization operator; one-parameter semigroup; potential; Poisson equation (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0842-6_5

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DOI: 10.1007/978-94-010-0842-6_5

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