Related papers: Operator NC functions

Let $f$ be a holomorphic function on the unit disc, and $(S_{n_{k}})$ be a subsequence of its Taylor polynomials about $0$. It is shown that the nontangential limit of $f$ and lim$_{k\rightarrow \infty }S_{n_{k}}$ agree at almost all points…

A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…

We introduce a notion of completely bounded holomorphic functions defined on the open unit ball of an operator space. We endow the set of these functions with an operator space structure, and in the scalar-valued case we identify an…

Let B be the Bergman projection associated to a domain on which the dbar-Neumann operator is compact. We show that arbitrary L^2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a…

For $\delta$ an $m$-tuple of analytic functions, we define an algebra $\hidg$, contained in the bounded analytic functions on the analytic polyhedron $ {|\delta^l(z)| < 1, \ 1 \leq l \leq m}$, and prove a representation formula for it. We…

We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains…

We study one class of continuous functions $f$ defined on segment $[0,1]$ by equality $$ f(x)=\delta_{\alpha_1(x)1}+\sum^{\infty}_{k=2}\left[\delta_{\alpha_k(x)k}\prod^{k-1}_{j=1}g_{\alpha_j…

An implicit operation of a class of similar algebras $\mathsf{K}$ is a collection of first order definable partial functions on the members of $\mathsf{K}$ that is globally preserved by homomorphisms. For instance, "taking inverses" can be…

We show that any differential operator of the form $L(y)=\sum_{k=0}^{k=N} a_{k}(x) y^{(k)}$, where $a_k$ is a real polynomial of degree $\leq k$, has all real eigenvalues in the space of polynomials of degree at most n, for all n. The…

The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…

We define analogues of higher derivatives for $F_q$-linear functions over the field of formal Laurent series with coefficients in $F_q$. This results in a formula for Taylor coefficients of a $F_q$-linear holomorphic function, a definition…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover,…

We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…

We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a…

We generalize our earlier results from \cite{K} on the Bessmertny\u{\i} class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…