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

In: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Author

Listed:
  • Dong Myung Chung

    (Sogang University, Department of Mathematics)

  • Un Cig Ji

    (Seoul National University, Global Analysis Research Center, Department of Mathematics)

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.

Suggested Citation

  • Dong Myung Chung & Un Cig Ji, 2001. "Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis," Springer Books, in: Luigi Accardi & Hui-Hsiung Kuo & Nobuaki Obata & Kimiaki Saito & Si Si & Ludwig Streit (ed.), Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, pages 89-100, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0842-6_5
    DOI: 10.1007/978-94-010-0842-6_5
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