Related papers: Generalized quaternionic Schur functions in the ba…

We characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions.

We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…

We apply a theorem of Geronimus to derive some new formulas connecting Schur functions with orthogonal polynomials on the unit circle. The applications include the description of the associated measures and a short proof of Boyd's result…

We make a broad conjecture about the $k$-Schur positivity of Catalan functions, symmetric functions which generalize the (parabolic) Hall-Littlewood polynomials. We resolve the conjecture with positive combinatorial formulas in cases which…

Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes A and B must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a…

We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced…

We present the fermionic representation for the q-deformed hypergeometric functions related to Schur polynomials considered by S.Milne \cite{Milne}. For $q=1$ these functions are also known as hypergeometric functions of matrix argument…

We compute the generating function of column-strict plane partitions with parts in {1,2,...,n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler's ["The major counting of nonintersecting…

The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…

We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the…

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a…

We continue the development of X-ray tomography in sub-Riemannian geometry. Using the Fourier Transform adapted to the group structure, we generalize the Fourier Slice Theorem to the class of H-type groups. The Fourier Slice Theorem…

The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to…

This paper studies the singularities of Cullen-regular functions of one quaternionic variable. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullen-regular functions are thus classified as removable,…

A sharp $L^p$ spectral multiplier theorem of Mihlin--H\"ormander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has…

The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In recent years, delving into the factorization of the second…

We show characterizations of the class of Cullen-regular functions in the sense of Gentili-Struppa for any domain $\Omega$ in terms of the Fueter operator. We then state a Integral Theorem and discuss how it can be used to define a more…

Let $A$ be a general expansive matrix and $X$ be a ball quasi-Banach function space on $\mathbb R^n$, whose certain power (namely its convexification) supports a Fefferman--Stein vector-valued maximal inequality and the associate space of…

We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms…