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A Bimonogenic Cauchy Transform on Higher Order Lipschitz Classes
We prove that a Cauchy transform naturally arising for bimonogenic Clifford algebra valued functions theory behaves invariant on the higher order...
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Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results
We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and...
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Bivariate Poly-analytic Hermite Polynomials
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier–Wigner transform of the...
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Local Maxima of White Noise Spectrograms and Gaussian Entire Functions
We confirm Flandrin’s prediction for the expected average of local maxima of spectrograms of complex white noise with Gaussian windows (Gaussian...
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Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator
Dynamic mode decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are discretized and examined using...
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Commuting Toeplitz Operators on Fock–Sobolev Spaces of Negative Orders
In the setting of Fock–Sobolev spaces of positive orders over the complex plane, Choe and Yang showed that if the one of the symbols of two commuting...
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Complements in Functional Analysis
Functional analysis deals with properties of spaces of functions (or of sequences), rather than of individual objects. To study a specific function...
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Interfaces in Spectral Asymptotics and Nodal Sets
This is a survey of results obtained jointly with Boris Hanin and Peng Zhou on interfaces in spectral asymptotics, both for Schrödinger operators on...
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Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation
Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac...
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Direct Scattering II
In this chapter the scattering process is described physically and mathematically, and the definition of the scattering operator is provided in terms...
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Translation-invariant Operators in Reproducing Kernel Hilbert Spaces
Let G be a locally compact abelian group with a Haar measure, and Y be a measure space. Suppose that H is a reproducing kernel Hilbert space of...
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Geometric Properties of Reproducing Kernels in Hilbert Spaces of Entire Functions
We give a survey of recent results about properties of systems of reproducing kernels in Paley–Wiener spaces, de Branges spaces and Fock spaces. In...
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Uncertainty Principles on Clifford Modules
In this paper, we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra, which heavily...
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Galilean Thermodynamics of Continua
We take the Relativity as model, process termed “geometrization”, but with Bargmann symmetry group, an extension of Galileo’s group acting on a...
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Hypercyclic exponential of the differential operator on Banach spaces related to Fock spaces
In this note, we give the mixing, and therefore hypercyclic, property of the exponential of the differential operator on Banach spaces related to...