Related papers: Intertwining operators between different Hilbert s…
The intertwining operator constructed in [Sz1,Sz2] does not appear in the right form. It is established there by using only the anticommutators. The correct operator must involve all endomorphisms, which are unified by the Z-Fourier…
We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
Controlled g-atomic subspace for a bounded linear operator is being presented and a characterization has been given. We give an example of controlled K-g-fusion frame. We construct a new controlled K-g-fusion frame for the Hilbert space H ?…
For a symmetric pair $(G,H)$ of reductive groups we extend to a large class of generalized principal series representations our previous construction of meromorphic families of symmetry breaking operators. These operators intertwine between…
In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum analogues of the Poisson and Radon transforms…
A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, $\{f_i\}_{i \in \sigma} \cup \{g_i\}_{i \in…
In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…
The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$…
General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…