0000000000433443

AUTHOR

Joachim Toft

showing 4 related works from this author

Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces

2017

We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, \(\mathcal{H}\), and its dual, \(\mathcal{H}^\prime\) . We prove that for such quasi-Banach space \(\mathcal{B}\), there are convenient Hilbert spaces, \(\mathcal{H}_{k}, k=1,2\), with normalized Hermite functions as orthonormal bases and such that \(\mathcal{B}\) lies between \(\mathcal{H}_1\; \mathrm{and}\;\mathcal{H}_2\), and the latter spaces lie between \(\mathcal{H}\; \mathrm{and}\;\mathcal{H}^\prime\).

CombinatoricsPhysicsMathematics::Functional Analysissymbols.namesakeHilbert manifoldMathematical analysisHilbert spacesymbolsOrthonormal basisHermite functionsSpace (mathematics)Prime (order theory)
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Mapping properties for the Bargmann transform on modulation spaces

2010

We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.

Mathematics::Functional AnalysisPure mathematicsModulation spaceFunctional analysisMathematics - Complex Variablesbijectivity propertiesApplied MathematicsSpectrum (functional analysis)Banach spaceOperator theoryComputer Science::Digital LibrariesVDP::Mathematics and natural science: 400::Mathematics: 410Algebraharmonic oscillatorhermite functionsBerezin–Toeplitz operatorsFOS: MathematicsInterpolation spaceBirnbaum–Orlicz spaceComplex Variables (math.CV)Lp spaceAnalysisMathematicsJournal of Pseudo-Differential Operators and Applications
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Remarks on mapping properties for the Bargmann transform on modulation spaces

2011

We investigate the mapping properties for the Bargmann transform and prove that this transform is isometricand bijective from modulation spaces to convenient Banach spaces of analytic functions.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsModulation spaceFunctional analysisApplied MathematicsBanach spaceBijectionInterpolation spaceLp spaceAnalysisHarmonic oscillatorAnalytic functionMathematicsIntegral Transforms and Special Functions
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Factorizations and Singular Value Estimates of Operators with Gelfand–Shilov and Pilipović kernels

2017

We prove that any linear operator with kernel in a Pilipović or Gelfand–Shilov space can be factorized by two operators in the same class. We also give links on numerical approximations for such compositions. We apply these composition rules to deduce estimates of singular values and establish Schatten–von Neumann properties for such operators. nivå2

Mathematics::Operator Algebras
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