Related papers: Mellin-Barnes presentations for Whittaker wave fun…
In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles.
In this paper we provide a unified approach to a family of integrals of Mellin--Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of…
We obtain certain Mellin-Barnes integrals which present wave functions for $GL(n,\mathbb{R})$ hyperbolic Sutherland model with arbitrary positive coupling constant.
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to…
We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed…
Using Zhelobenko-Stern formulas for the action of the generators of orthogonal Lie algebra in corresponding Gelfand-Tsetlin basis, we derive Mellin-Barnes presentations for the wave functions of $B_n$ Toda lattice. They are in accordance…
Intertwiners between representations of Lie groups can be used to obtain relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular raising operators…
It is shown that Mellin transforms of p-adic Whittaker functions exist for generic characters. For good choices of vectors they are rational functions. For class one vectors they can be calculated explicitly. It turns out that they are…
Considering the relationship between two bases in representation space of the three-dimensional proper Lorentz group, we derive some formulas with integrals involving Coulomb wave functions, which can be considered as Fourier, Mellin,…
Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define…
Recently we found Mellin-Barnes integrals, representing the wave function for $GL(n,\mathbb{R})$ hyperbolic Sutherland model. In present paper, we establish bispectral properties of this wave function with respect to dual…
In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules and the set…
In this paper, we present a new approach to the construction of Mellin-Barnes representations for Feynman integrals inspired by the Method of Brackets. The novel technique is helpful to lower the dimensionality of Mellin-Barnes…
We prove wave breaking (shock formation) for some Whitham-type equations which include the Burgers-Hilbert equation, the fractional Korteweg-de Vries equation, and the classical Whitham equation. The result seems to be new for the…
In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this…
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the…
We introduce techniques to treat numerically Mellin-Barnes integrals in physical regions, which arise in the need of the computation of Feynman integrals for the electroweak two-loop corrections to the pseudo observables at the Z-boson…