Function with fractal characteristics can be obtained using periodic components and all these components are band-limited functions. Then, we can consider the conditions for the application of the ShannonWhittaker theorem for the case of prefractal signals. Also, we relate such theorem with the order of the prefractal signal. For such studies, we use an expression of the sampling theorem for pe...

We construct the action of the quantum group Uv(sln) by the natural correspondences in the equivariant localized K-theory of the Laumon based Quasiflags’ moduli spaces. The resulting module is the universal Verma module. We construct geometrically the Shapovalov scalar product and the Whittaker vectors. It follows that a certain generating function of the characters of the global sections of th...

Let ψ be a smooth character of a closed subgroup, H, of a reductive p-adic group G. If P is parabolic subgroup of G such that PH is open in G, we define the constant term of every smmoth fubction on G which transforms by ψ under the right action of G. The example of mixed models is given: it includes symmetric spaces and Whittaker models. In this case a notion of cuspidal function is defined an...

Two explicit guard functions Kj = Kj(δz), j = 1, 2, are obtained, which depend on the distance δz between z and the nearest point of the integer lattice in the complex plane, such that δzK1(δz) ≤ |σ(z)|e−π|z|2/2 ≤ δzK2(δz), z ∈ C, where σ(z) stands for the Weierstraß σ-function. This result is used to improve the circular truncation error upper bound in the qth order Whittaker-type derivative s...

We prove that the exact reconstruction of a function s from its samples s(xi) on any “sufficiently dense” sampling set {xi}i∈Λ can be obtained, as long as s is known to belong to a large class of spline-like spaces in Lp(Rn). Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Sh...

This article grew out of my talk in ‘The Legacy of Srinivasa Ramanujan’ conference where I spoke about some techniques to prove algebraicity results for the special values of symmetric cube L-functions attached to the Ramanujan ∆-function. If one wishes to compare these different techniques, then one needs to compare various automorphic periods attached to the symmetric cube transfer of ∆. Moti...

In this note we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Corresponding Whittaker functions are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gamma-functions. This property is one of the manifestations of an interesting connection between MellinBarnes and Givental integral representations of Whittaker functions. Th...

An alternative way of understanding physical effects in curved space time is to solve the associated particle equation such as Dirac equation. It a first-order relativistic wave and defines spin-1/2 massive particles like electrons quarks. In this study, we solved an anisotropic rainbow universe. Subsequently, reduced obtained by making use asymptotic property Whittaker function. final stage, c...

We construct a geometric lifting of the Burge correspondence as composition local birational maps on generic Young-diagram-shaped arrays. establish its fundamental relation to Robinson-Schensted-Knuth and Sch\"utzenberger involution. also show number properties correspondence, specializing them case symmetric input In particular, our construction shows that such mapping is volume preserving in ...