The Experts below are selected from a list of 10086 Experts worldwide ranked by ideXlab platform
Zhengyu Mao - One of the best experts on this subject based on the ideXlab platform.
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A Whittaker-Plancherel Inversion Formula for SL(2, R) ✩
Journal of Functional Analysis, 2006Co-Authors: Ehud Moshe Baruch, Zhengyu MaoAbstract:Abstract We prove a Whittaker–Plancherel Inversion Formula which gives a Whittaker coefficient of a function on SL ( 2 , R ) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov Inversion Formula play a central role in the proof of this Whittaker–Plancherel Inversion Formula.
Ehud Moshe Baruch - One of the best experts on this subject based on the ideXlab platform.
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A Whittaker-Plancherel Inversion Formula for SL(2, R) ✩
Journal of Functional Analysis, 2006Co-Authors: Ehud Moshe Baruch, Zhengyu MaoAbstract:Abstract We prove a Whittaker–Plancherel Inversion Formula which gives a Whittaker coefficient of a function on SL ( 2 , R ) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov Inversion Formula play a central role in the proof of this Whittaker–Plancherel Inversion Formula.
Dalimil Mazac - One of the best experts on this subject based on the ideXlab platform.
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A Crossing-Symmetric OPE Inversion Formula
Journal of High Energy Physics, 2019Co-Authors: Dalimil MazacAbstract:We derive a Lorentzian OPE Inversion Formula for the principal series of $sl(2,\mathbb{R})$. Unlike the standard Lorentzian Inversion Formula in higher dimensions, the Formula described here only applies to fully crossing-symmetric four-point functions and makes crossing symmetry manifest. In particular, inverting a single conformal block in the crossed channel returns the coefficient function of the crossing-symmetric sum of Witten exchange diagrams in AdS, including the direct-channel exchange. The Inversion kernel exhibits poles at the double-trace scaling dimensions, whose contributions must cancel out in a generic solution to crossing. In this way the Inversion Formula leads to a derivation of the Polyakov bootstrap for $sl(2,\mathbb{R})$. The residues of the Inversion kernel at the double-trace dimensions give rise to analytic bootstrap functionals discussed in recent literature, thus providing an alternative explanation for their existence. We also use the Formula to give a general proof that the coefficient function of the principal series is meromorphic in the entire complex plane with poles only at the expected locations.
Wenchang Sun - One of the best experts on this subject based on the ideXlab platform.
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Inversion Formula for the Windowed Fourier Transform
arXiv: Functional Analysis, 2010Co-Authors: Wenchang SunAbstract:In this paper, we study the Inversion Formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an Inversion Formula which is known in engineering. We show that the integral involved in the Formula is convergent almost everywhere on $\bbR$ as well as in $L^p$ for all $1
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Inversion Formula for the windowed fourier transform
arXiv: Functional Analysis, 2010Co-Authors: Wenchang SunAbstract:In this paper, we study the Inversion Formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an Inversion Formula which is known in engineering. We show that the integral involved in the Formula is convergent almost everywhere on $\bbR$ as well as in $L^p$ for all $1
David Simmonsduffin - One of the best experts on this subject based on the ideXlab platform.
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a spacetime derivation of the lorentzian ope Inversion Formula
Journal of High Energy Physics, 2018Co-Authors: David Simmonsduffin, Douglas Stanford, Edward WittenAbstract:Caron-Huot has recently given an interesting Formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this Formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian Inversion Formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.
