Related papers: The Integral Transform of N.I.Akhiezer
We study a class of arrangements of lines with multiplicities on the plane which admit the Chalykh-Veselov Baker-Akhiezer function. These arrangements are obtained by adding multiplicity one lines in an invariant way to any dihedral…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different…
I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
We consider mapping properties of the iterated Stieltjes transform, establishing its new relations with the iterated Hilbert transform (a singular integral) on the half-axis and proving the corresponding convolution and Titchmarsh's type…
This paper has been withdrawn by the author(s). The material contained in the paper will be published in a subtantially reorganized form, part of it is now included in math.QA/0510174
This is a chapter for the book "Understanding Quantum Phase Transitions" edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010)
In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…
The study of $n$-dimensional inverted Kloosterman sums was suggested by Katz (1995) who handled the case when $n=1$ from complex point of view. For general $n\geq 1$, the $n$-dimensional inverted Kloosterman sums were studied from both…
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
Very first time Elzaki transform is used in non relativistic quantum mechanics to solve $N$-dimensional Schr\"{o}dinger equation in a closed form for different solvable potential models. A universal transformation scheme is introduced and a…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
An alternative Lagrangian definition of an integrable defect is provided and analyzed. The new approach is sufficiently broad to allow a description of defects within the Tzitzeica model, which was not possible in previous approaches, and…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical…
This is an expanded version of the talk I gave at Oberwolfach, MIT and several other universities.
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…