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On Joint Fourier–Laplace Transforms
Communications in Statistics - Theory and Methods, 2010Weak convergence of random variables is characterized by pointwise convergence of the Fourier transform of the respective distributions, and in some cases can also be characterized through the Laplace transform. For some distributions, the Laplace transform is easier to compute and provides an alternative approach to the method of characteristic ...
Patrick Fitzsimmons, Tucker McElroy
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Fourier-Laplace transforms decaying exponentially
Mathematical Proceedings of the Cambridge Philosophical Society, 1988Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:where θ is a constant with –π/2 ≤ θ ≤ π/2.
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WEIGHTED FOURIER-LAPLACE TRANSFORMS OF ANALYTIC FUNCTIONALS ON THE DISK
Russian Academy of Sciences. Sbornik Mathematics, 1994Summary: A study is made of the question as to whether the space \(\widehat L^ a_ 2(D,\mu)\) has a norm of the form \[ \|\widehat f\|_ \nu= \int^ \infty_ 0 \int^{2\pi}_ 0 | \widehat f(xe^{i\theta})|^ 2d\nu(xe^{i\theta}) \] equivalent to the norm \[ \|\widehat f\|_{\widehat L^ a_ 2(D,\mu)}\overset{\text{def}}= \| f\|_{L^ a_ 2(D,\mu)}, \] where \(\nu ...
Napalkov, V. V., Yulmukhametov, R. S.
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A generalized transform, grouping, Fourier, Laplace and Z transforms
The 14th International Conference on Microelectronics,, 2004The following is a summary description of some research results that were taught to students over many years and communicated by the author in IEEE Proceedings submission, in the book proposals, and poster sessions. A generalized transform, grouping Fourier and Laplace transform in the continuous-time domain and Fourier and z transform in the discrete ...
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A note on holomorphic functions and the Fourier-Laplace transform
MATHEMATICA SCANDINAVICA, 2017We revisit the classical problem of when a given function, which is analytic in the upper half plane $\mathbb{C} _+$, can be written as the Fourier transform of a function or distribution with support on a half axis $(-\infty ,b]$, $b\in \mathbb{R} $.
Marcus Carlsson, Jens Wittsten
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The Fourier, Laplace, and z-Transforms
2017The study of signals and systems can be carried out in terms of either a time-domain or a transform-domain formulation. The transform-domain approach to signals and systems is based on the transformation of functions using the Fourier, Laplace, and z-transforms. This chapter deals with the Fourier transform (FT), which can be viewed as a generalization
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Tables of Fourier, Laplace and Hankel Transforms of (u,n)-Dimensional Generalized Functions
Acta Applicandae Mathematica, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aguirre Téllez, Manuel A. +2 more
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Growth properties of plurisubharmonic functions related to Fourier-Laplace transforms
Journal of Geometric Analysis, 1998The purpose of the paper is to study the behavior at infinity of Fourier-Laplace transforms of distributions or more generally plurisubharmonic functions \(u\) in \({\mathbb C}^n\), \(u\in PSH({\mathbb C}^n)\). If \(H\) is a supporting function in \({\mathbb R}^n\), that is, \(H\) is convex and positively homogeneous of degree 1, then \(P_H\) will ...
Hörmander, Lars, Sigurdsson, Ragnar
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Note on the Fourier-Laplace Transform of $\overline{\partial}$-Cohomology Classes
Zeitschrift für Analysis und ihre Anwendungen, 1998We construct the inverse of the Fourier-Laplace transform of \overline{\partial} -cohomology classes (of (n, n–1) -forms) in the complement of a convex compact set ...
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