Related papers: The finite Fourier Transform and projective 2-desi…
Framework for constructing Fock spaces associated either with certain solutions of the quantum Yang-Baxter equation or with infinite dimensional Hecke algebra is presented. For the former case, the quantum deformed oscillator algebra…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
We describe two new combinatorial algorithms (using the language of "triangular arrays") for computing the Fourier transforms of simple perverse sheaves on the moduli space of representations of an equioriented quiver of type A. (A rather…
We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint…
We consider one dimensional deformed Heisenberg algebra leading to existence of minimal length for coordinate operator and minimal and maximal uncertainty of momentum operator. For this algebra an exactly solvable Hamiltonian is…
Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers z_{n}, and of an arbitrary additional parameter (a respectively q), and provide finite-dimensional representations of the two…
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally…
A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations, with a…
Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow…
Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of…
We study tight projective 2-designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2-design in every dimension. Pandey, Paulsen, Prakash, and Rahaman recently proposed…
We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate…
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…