Related papers: Factorization of the Shoenfield-like bounded funct…

An explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained that makes Schwarzian functional integrals calculus simpler and more transparent.

A 2-category was introduced in arXiv:0803.3652 [math.QA] that categorifies Lusztig's integral version of quantum sl(2). Here we construct for each positive integer N arepresentation of this 2-category using the equivariant cohomology of…

The functional Schr\"odinger representation of a scalar field on an $n$-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical…

In this note a Fuglede type theorem is proved for Fourier multiplier operators on translation invariant Banach function spaces with order continuous norm over compact abelian groups.

We examine translation invariant operators on the Polyanalytic Sobolev-Fock spaces and show that they take the form \begin{align*} S_{\phi} F(z) = \int_{\mathbb{C}^n} F(w)e^{\pi z\cdot \overline{w}}\phi(w-z,\overline{w}-z) e^{\pi |w|^2}\,…

We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial,…

In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices -- factored as PSD $\times$ unitary -- to any vector field $F:\mathbb{R}^d\rightarrow \mathbb{R}^d$. The theorem, known as the polar…

The soft-collinear effective theory has been recently applied to prove novel factorization theorems for many B decays. We describe here in some detail the factorization relation for color-supressed nonleptonic B -> D(*)0 pi0 decays and…

We prove the non-commutative analogue of Grothendieck's Standard Conjecture D for the dg-category of matrix factorizations of an isolated hypersurface singularity in characteristic 0. Along the way, we show the Euler pairing for such…

The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theorem for bounded holomorphic functions on the unit disk.

We prove a tamely ramified version of the Kazhdan-Lusztig equivalence using factorization algebras. More precisely, we establish an equivalence between the DG category of Iwahori-integrable affine Lie algebra representations and the DG…

Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of fractions. Under the assumption that K contains all r-th roots of unity for an integer r, we prove that, given an…

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in…

We prove a Kn"orrer periodicity type equivalence between derived factorization categories of gauged LG models, which is an analogy of a theorem proved by Shipman and Isik independently. As an application, we obtain a gauged LG version of…

We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson--Ikeda--Matsumura--Naruse and by Hudson--Matsumura.

Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…

We show that some matrices are Schur multipliers and this is applied to obtain classes of operator-valued Foguel-Hankel operators similar to contractions. This provides partial answers to a problem of K. Davidson and the second author…

Soft-collinear effective theory is used to prove factorization of the B->gamma+l+nu decay amplitude at leading power in Lambda/m_b, including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution…

The equivalence between the approaches of Drinfeld-Sokolov and Feigin-Frenkel to the mKdV hierarchies is established. A new derivation of the mKdV equations in the zero curvature form is given. Connection with the Baker-Akhiezer function…

We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…