Related papers: Functional integration over the factor-space $Diff…
A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of…
We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…
A Lie theoretic interpretation is given for some formulas of Schur functions and Schur $Q$-functions. Two realizations of the basic representation of the Lie algebra $A^{(2)}_2$ are considered; one is on the fermionic Fock space and the…
In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo, I. Sabadini, Krein-Langer factorization and related topics…
We introduce generalized Schur functions and generalized positive functions in setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces
We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here…
In our last work, we formulate a Fourier transformation on the infinite-dimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution $\exp(-\pi…
We obtain explicit expressions for differential operators defining the action of the Virasoro algebra on the space of univalent functions. We also obtain an explicit Taylor decomposition for Schwarzian derivative and a formula for the…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…
We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…
We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion…
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributions. In this paper, we are interested in pairs of…
We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real…
The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the…
We prove a representation formula for superharmonic functions on the half-space $\mathbb{R}^N_+ := \mathbb{R}^{N-1}\times]0,+\infty[$. As a consequence, we derive some comparison principles and various positivity results.
The theoretical and experimental evidence regarding the use of (J + 1/2) squared and J(J + 1) as a functional in formulae for rotational term values in the spectral analysis of a diatomic molecule in electronic state singlet-Sigma is…
We consider different characterizations of Triebel--Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss…
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…