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Berezin Transform, Mellin Transform and Toeplitz Operators
Complex Analysis and Operator Theory, 2010Let \(B\) be the Berezin transform associated with the Bergman space. The authors of the article under review improve a theorem of \textit{P. Ahern} [J. Funct. Anal. 215, No. 1, 206--216 (2004; Zbl 1088.47014)]. Namely, they show that, if \(u\in L^1\) and \(Bu\) is a harmonic function, then \(u\) itself is harmonic.
Čučković, Željko, Li, Bo
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2009
This table contains Mellin transforms to supplement the ones at the end of Chap. 1. These are still a small fraction of the transforms that are listed in Marichev (1983). The special functions that are not commonly used are defined in Appendix B. The value of n is an integer in the transforms below.
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This table contains Mellin transforms to supplement the ones at the end of Chap. 1. These are still a small fraction of the transforms that are listed in Marichev (1983). The special functions that are not commonly used are defined in Appendix B. The value of n is an integer in the transforms below.
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Multipliers for the Mellin Transformation
Canadian Mathematical Bulletin, 1978AbstractIn this paper we generalize the Mellin multiplier theorem we proved earlier [8] to spaces with quite general weights, satisfying an Ap-type condition. Applications are made to the Hilbert transformation.
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The mellin-whittaker integral transform
Mathematical Notes of the Academy of Sciences of the USSR, 1986The author gives an inversion formula for the integral transform \(\iint K(\xi,\eta,\alpha,\beta,\lambda)f(\xi,\eta,\lambda)d\xi d\eta =F(\alpha,\beta,\lambda)\) with the kernel \[ K=\{(2\lambda)^{2i\alpha +1}B(i(\alpha +\beta)+1/2,i(\alpha -\beta)+1/2)/_{2\Gamma (2i\alpha +1)}\}\cdot \] \[ \eta^{2i}e^{\beta \pi sign \xi \eta -i\lambda \xi \eta}\Phi (i(
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2009
Generally speaking, unlike the Fourier and Laplace transforms, we find that the Mellin transform is not very useful in a direct manner. It is quite effective, however, in the derivation of certain properties of integrals, in summing series, and in statistics.
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Generally speaking, unlike the Fourier and Laplace transforms, we find that the Mellin transform is not very useful in a direct manner. It is quite effective, however, in the derivation of certain properties of integrals, in summing series, and in statistics.
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2002
In this and the next chapter, we study the Mellin transform, which, while closely related to the Fourier transform, has its own peculiar uses. In particular, it turns out to be a most convenient tool for deriving asymptotic expansions, although it has other applications ...
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In this and the next chapter, we study the Mellin transform, which, while closely related to the Fourier transform, has its own peculiar uses. In particular, it turns out to be a most convenient tool for deriving asymptotic expansions, although it has other applications ...
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Mellin Transforms in Summation
1978Suppose we wish to evaluate the sum $$ S = \sum\limits_{n = 1}^\infty {f(n)} $$ (1) .
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From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing
Physical Review D, 2021Charlotte Sleight, Massimo Taronna
exaly
Bootstrapping inflationary correlators in Mellin space
Journal of High Energy Physics, 2020Charlotte Sleight, Massimo Taronna
exaly