Spaces of test and generalized functions in Problems of Infinite Dimensional Analysis
V. A. Tesko
PhD-thesis abstract, Institute of Mathematics NAS of Ukraine, Kyiv, 2005, 1-16 p.PhD Thesis Abstract (.pdf)
The thesis is devoted to the subsequent development of the biorthogonal approach to a construction of the theory of generalized functions of infinite many variables. Operators (on Fock spaces) that generated by the annihilation and creation operators are constructed and studied. Spaces of test and generalized functions are studied with using these operators. A family of generalized translation operators on the test functions spaces is constructed. An orthogonal approach to the construction of the theory of generalized functions of infinite many variables is developed. This approach is applied to the study of the Poissonian white noise analysis.