Related papers: The Integral Transform of N.I.Akhiezer
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
In this lecture results on the Berezin-Toeplitz quantization of arbitrary compact quantizable Kaehler manifolds are presented. These results are obtained in joint work with M. Bordemann and E. Meinrenken. The existence of the…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.
For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.
We study basic properties of the generalized ideal transforms $D_I(M, N)$ and the set of associated primes of the modules $R^iD_I(M,N).$
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
In this paper, we investigate the "angular changes" behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts…
Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
This is mainly a translation of Proc. of the 29th Symp. on History of Mathematics, Tsuda University, held Oct. 2018, of my talk. The first occasion when I studied the history of the theory of invariant integrals (or measures) was an…