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Bargmann-Type Transforms and Modified Harmonic Oscillators
We study some complete orthonormal systems on the real line. These systems are determined by Bargmann-type transforms, which are Fourier integral...
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Planar Sampling Sets for the Short-Time Fourier Transform
This paper considers the problem of restricting the short-time Fourier transform to sets of nonzero measure in the plane. Thereby, we study under...
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On pair correlation of Hermite coefficients of functions from the Hardy class
Assuming that a function and its Fourier transform are dominated by a Gaussian, Vemuri found a sharp estimate for the decay rate of the Hermite...
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On the connection between uniqueness from samples and stability in Gabor phase retrieval
Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible...
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Nonuniform multiresolution analysis associated with linear canonical transform
The linear canonical transform (LCT) has attained respectable status within a short span and is being broadly employed across several disciplines of...
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Gaussian RBF kernels via Fock spaces: quaternionic and several complex variables settings
In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock...
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Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order
In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart...
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Radial Operators on Polyanalytic Bargmann–Segal–Fock Spaces
This paper considers bounded linear radial operators on the polyanalytic Fock spaces \(\mathcal {F}_n\) and on the true-polyanalytic Fock...
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Windowed special affine Fourier transform
With the aim to circumvent the limitations of the special affine Fourier transform, we introduce a novel time–frequency transform namely the...
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Zeros of the Wigner distribution and the short-time Fourier transform
We study the question under which conditions the zero set of a (cross-) Wigner distribution W ( f , g ) or a short-time Fourier transform is empty. This...
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Nonlinear Coherent States Associated with a Measure on the Positive Real Half Line
We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated...
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The generalized Toeplitz operators on the Fock space \(F_\alpha ^2\)
Let μ be a positive Borel measure on the complex plane ℂ n and let j = ( j 1 , …, j n ) with j i ∈ ℕ. We study the generalized Toeplitz operators
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