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Bargmann Transform on the Space of Hyperplanes
We introduce an integral transform on the space of hyperplanes applying the Plancherel formula of the Radon transform to the definition of the...
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Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise
We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the...
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On a New Characterization of the True-Poly-Analytic Bargmann Spaces
We consider a novel bounded integral transform with a kernel function being the n -th polyanalytic Intissar–Hermite polynomial. We provide a concrete...
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Segal–Bargmann Transforms Associated to a Family of Coupled Supersymmetries
The Segal–Bargmann transform is a Lie algebra and Hilbert space isomorphism between real and complex representations of the oscillator algebra. The...
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Resolvent Algebra in Fock-Bargmann Representation
The resolvent algebra \(\mathfrak {R}\left( X, \sigma \right) \)...
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Unbounded Operators on the Segal–Bargmann Space
In this paper we analyse the domains of differential and multiplication operators on the Segal–Bargmann space. We consider the basic estimate for the...
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The Segal–Bargmann Transform in Clifford Analysis
The Segal–Bargmann transform plays an essential role in signal processing, quantum physics, infinite-dimensional analysis, function theory and...
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The Bicomplex Dual Fractional Hankel Transform
We provide a concrete characterization of the Bergman space of bicomplex-valued bc-meromorphic functions with a strong pole at the origin of the...
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Cross-Toeplitz operators on the Fock–Segal–Bargmann spaces and two-sided convolutions on the Heisenberg group
We introduce an extended class of cross-Toeplitz operators which act between Fock–Segal–Bargmann spaces with different weights. It is natural to...
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A Note on the Completeness of Generalized Eigenfunctions of the Hamiltonian of Reggeon Field Theory in Bargmann Space
The aim of the present paper is to review some old results of Intissar (Commun Math Phys 113:263–297, 1987) and to study some new spectral properties...
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On the Quaternionic Short-Time Fourier and Segal–Bargmann Transforms
In this paper, we study a special one-dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice...
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Metamorphism as a covariant transform for the SSR group
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism...
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A sparse approximation for fractional Fourier transform
The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert...