arXiv subjects

D. Perisic

Publications and source records attributed to D. Perisic.

3 recordsLinked to original sources

arXiv2007

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 Gelfand-Shilov spaces, of Roumieu and Beurling type.

quant-ph↗

arXiv2007

Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions

We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test space of tempered ultradistributions of Beurling - Komatsu type can be identified with the space of sequences of ultrapolynomal falloff and its dual space with the space of sequences of ultrapolynomial growth. As a consequence of the Kernel theorem we have that the Weyl transform can be extended on a space of tempered ultradistributions of Beurling - Komatsu type.

math.FA↗

arXiv2007

Hermite Expansions of Elements of Generalized Gelfand-Shilov space

We characterize the elements of generalized Gelfand Shilov spaces in terms of the coefficients of their Fourier-Hermite expansion. The technique we use can be applied both in quasianalytic and nonquasianalytic case. The characterizations imply the kernel theorems for the dual spaces. The cases when the test space is quasianalytic are important in quantum field theory with a fundamental length, see for example papers of E.Bruning and S.Nagamachi,where it was conjectured that the properties of the space of Fourier hyper functions, which is isomorphic with S^1_1 are well adapted for the use in the theory.

quant-ph↗