Relationships between usual and exotic Hida–Kubo–Takenaka spaces

Abstract

In this paper, we discuss the relationships between exotic Hida–Kubo–Takenaka space and usual Hida distributions. We also discuss an example that implies is an Cesàro Hilbert space constructed from the Hilbert space generated by delta functions, and demonstrate a well-known equality in white noise theory in our settings.

Keywords:

• white noise theory
• Lévy Laplacian
• exotic Laplacian
• Gross Laplacian

Keywords:

• 60H40

Acknowledgements

The author wishes to express his sincere gratitude to Prof. N. Obata and Prof. K. Saito for their helpful advices and comments. The author is also grateful to the organizers of this conference for the opportunity.