Related papers: Noncommutative peak interpolation revisited
We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…
This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
Recent concurrent work by Dupr\'{e} la Tour and Fujii and by Hollender, Manurangsi, Meka, and Suksompong [ITCS'26] introduced a generalization of classical discrepancy theory to non-additive functions, motivated by applications in fair…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main…
The Hilbert function of standard graded algebras are well understood by Macaulay's theorem and very little is known in the local case, even if we assume that the local ring is a complete intersection. An extension to the power series ring…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…
The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of H\"ormander of the functions/distributions of…
Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal algebra of $\mathcal{M}$. We prove Stein-Weiss type interpolation theorem of Haagerup…
We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…
We develop the theory of the higher commutator for Taylor varieties. A new higher commutator operation called the hypercommutator is defined using a type of invariant relation called a higher dimensional congruence. The hypercommutator is…
We describe the set of inner functions of finite order in a multi-connected domain, then we consider an optimization formulation of the Pick-Nevanlinna interpolation problem, and we generalize it to Hermite type interpolation.
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…