Compactness is established for pseudo-differential operators whose symbols lie in the refined modulation space M^{sharp,q} (0 < q ≤ 1) when acting on a broad family of modulation spaces.
Gelfand-Shilov spaces, Structural and Kernel theorems
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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.
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math.FA 2verdicts
UNVERDICTED 2representative citing papers
Proves that bilinear pseudo-differential operators with Gevrey-Hörmander symbols are invariant and continuous on modulation spaces, implying continuity on anisotropic Gelfand-Shilov spaces for both Beurling and Roumieu classes.
citing papers explorer
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Compactness for pseudo-differential and Toeplitz operators on modulation spaces
Compactness is established for pseudo-differential operators whose symbols lie in the refined modulation space M^{sharp,q} (0 < q ≤ 1) when acting on a broad family of modulation spaces.
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Bilinear pseudo-differential operators with Gevrey-H\"ormander symbols
Proves that bilinear pseudo-differential operators with Gevrey-Hörmander symbols are invariant and continuous on modulation spaces, implying continuity on anisotropic Gelfand-Shilov spaces for both Beurling and Roumieu classes.