Related papers: Fundamental Agler Decompositions
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In…
The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…
In this article we will give a affirmative answer to Gilbert's conjecture on Hardy spaces of Clifford analytic functions in upper half-space of $\mathbb{R}^8$. It depends on a explicit construction of Spinor space $\mathcal{R}_8$ and…
We introduce \`a la Vasilevski the weighted poly-Bergman spaces in the unit disc and provide concrete orthonormal basis and give close expression of their reproducing kernel. The main tool in the description if these spaces is the so-called…
We characterize the polynomial decay of orbits of Hilbert space $C_0$-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in the paper by C.J.K.Batty…
We introduce a natural generalization of a well studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give…
We extend Agler's notion of a function algebra defined in terms of test functions to include products, in analogy with the practice in real algebraic geometry, and hence the term preordering in the title. This is done over abstract sets and…
We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves…
In scalar-valued Hardy space, the class of Schmidt subspaces for a bounded Hankel operator are closely related to nearly $S^*$-invariant subspaces, as described by G\'{e}rard and Pushnitski. In this article, we prove that these subspaces in…
A Helson-Lowdenslager type result has been proved by Chen in the context of Lebesgue spaces of the unit circle equipped with a continuous rotationally symmetric norm by studying the simply invariant subspaces of the operator of…
We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra $\mathcal A\subseteq \mathcal B(\mathscr X)$ which…
In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our…
We construct an example to show that no condition of slow decrease of the modulus of a function is sufficient to make it cyclic in the Hardy space of the bidisc. This is similar to what is well known in the case of the Hardy space of the…
It is known that pure row contractions with one-dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard $d$-shift acting on the full Fock space. Upon settling for a softer relation than unitary…
We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…
It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the…
We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…
In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like…