0000000000179013

AUTHOR

Zdzislaw Suchanecki

showing 4 related works from this author

Explicit form of the time operator of a gaussian stationary process

2004

We present the time operator theory in the framework of stationary stochastic processes. The main results of the paper is the derivation of the time operator acting on the Fock space associated with a discrete time gaussian stationary process.

Semi-elliptic operatorStationary processPhysics and Astronomy (miscellaneous)Multiplication operatorGeneral MathematicsMathematical analysisDisplacement operatorOrnstein–Uhlenbeck processStationary sequenceShift operatorMathematicsOrder of integration
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Inner functions and local shape of orthonormal wavelets

2011

Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.

Pure mathematicsHardy spacesApplied MathematicsMathematical analysisWavelet transformHardy spaceLinear subspacesymbols.namesakeGeneralized Fourier seriesWaveletOrthonormal waveletssymbolsOrthonormal basisInvariant (mathematics)OrthonormalityInner functionsMathematicsApplied and Computational Harmonic Analysis
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Nonlocalization Properties of Time Operators Transformations

2014

It is presented a general approach to the problem of extension of time operators and the associated Lambda transformations on singular measures. It is also shown that Lambda transformations defined on function spaces having the Urysohn property are non localized. Particular attention has been devoted to time and Lambda operators associated with the Walsh-Paley system and to a characterization of their domain and non locality.

AlgebraPure mathematicsProperty (philosophy)Physics and Astronomy (miscellaneous)Function spaceGeneral MathematicsExtension (predicate logic)Characterization (mathematics)Operator theoryLambdaShift operatorDomain (mathematical analysis)MathematicsInternational Journal of Theoretical Physics
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Evolution semigroups and time operators on Banach spaces

2010

AbstractWe present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.

Unbounded operatorMathematics::Functional AnalysisBanach spaceSchauder basisApproximation propertyNuclear operatorApplied MathematicsTime operatorFinite-rank operatorBanach manifoldOperator theoryAlgebraInterpolation spaceC0-semigroupInnovationAnalysisMathematicsMathematicsofComputing_DISCRETEMATHEMATICSJournal of Mathematical Analysis and Applications
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