Hermite Expansions of Elements of Generalized Gelfand-Shilov space

Gelfand-Shilov spaces, Structural and Kernel theorems

It was shown recently that the space isomorphic with an Gelfand Shilov space is well adapted for the use in quantum field theory with a fundamental length. It is our believe that all Gelfand Shilov spaces, especially those with quasianalytic test function spaces, are good domains for the quantum field theory. The theory requires technical results from the theory of generalized functions and not merely differential calculus and well defined Fourier transform, but also the kernel theorem and the structural theorem. In the paper we give the structural (regularity) theorem and kernel theorem for G…

Inclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces

We prove that the Moyal multiplier algebras of the generalized Gelfand-Shilov spaces of type $S$ contain Palamodov spaces of type $\mathcal E$ and the inclusion maps are continuous. We also give a direct proof that the Palamodov spaces are algebraically and topologically isomorphic to the strong duals of the spaces of convolutors for the corresponding spaces of type $S$. The obtained results provide an effective way to describe the properties of pseudodifferential operators with symbols in the spaces of type $\mathcal E$.

Wigner 和 Gabor 相空间分析用于演化方程的传播算子

Wigner and Gabor phase-space analysis of propagators for evolution equations

本文通过Wigner和Gabor相空间分析，研究了演化方程传播算子的性质，推导了相关核的显式表达式并分析了Gabor矩阵的衰减特性。