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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
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Bootstrapping inflationary correlators in Mellin space
Journal of High Energy Physics, 2020Charlotte Sleight, Massimo Taronna
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A Mellin space approach to cosmological correlators
Journal of High Energy Physics, 2020Charlotte Sleight
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