Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition. (English) Zbl 1050.60070
Summary: Duality is established for new spaces of entire functions in two infinite-dimensional variables with certain growth rates determined by Young functions. These entire functions characterize the symbols of generalized Fock space operators. As an application, a proper space is found for a solution to a normal-ordered white noise differential equation having highly singular coefficients.
MSC:
| 60H40 | White noise theory |
| 46E50 | Spaces of differentiable or holomorphic functions on infinite-dimensional spaces |
| 47N30 | Applications of operator theory in probability theory and statistics |
Keywords:
Fock space; operator symbol; infinite-dimensional holomorphy; normal-ordered white noise differential equation; quantum white noiseReferences:
| [1] | DOI: 10.1142/S0219025701000498 · Zbl 1106.46306 · doi:10.1142/S0219025701000498 |
| [2] | Asai N., Hiroshima Math. J. 31 pp 299– (2001) |
| [3] | DOI: 10.1142/S0219025798000296 · Zbl 0928.60088 · doi:10.1142/S0219025798000296 |
| [4] | DOI: 10.1142/S0129055X0200117X · Zbl 1027.60072 · doi:10.1142/S0129055X0200117X |
| [5] | DOI: 10.1142/S0219025798000053 · Zbl 0918.60027 · doi:10.1142/S0219025798000053 |
| [6] | DOI: 10.1006/jfan.1999.3518 · Zbl 0969.46018 · doi:10.1006/jfan.1999.3518 |
| [7] | Ji U. C., M. Gräbner pp 203– (2000) |
| [8] | Krée P., Ann. Inst. H. Poincaré 18 pp 41– (1978) |
| [9] | DOI: 10.2969/jmsj/05130613 · Zbl 1157.81323 · doi:10.2969/jmsj/05130613 |
| [10] | Ouerdiane H., Japan. J. Math. 20 pp 187– (1994) |
| [11] | Ouerdiane H., Japan. J. Math. 21 pp 223– (1995) |
| [12] | Ouerdiane H., Nagoya Math. J. 151 pp 107– (1998) · Zbl 0921.60036 · doi:10.1017/S0027763000025204 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
