Related papers: Average operators on rectangular Herz spaces
Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromorphic) sections only as_partial operators_: they are defined…
We consider a random family of Schr\"odinger operators on a cover $X$ of a compact Riemannian manifold $M = X/\Gamma$. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and…
We introduce the $\lambda$-mean transform $M_{\lambda}(T)$ of a Hilbert space operator $T$ as an extension of some operator transforms based on the Duggal transform $T^D$ by $M_{\lambda}(T) := \lambda T + (1-\lambda)T^D$, and present some…
We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the…
Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
We characterize bounded multiplication operators in weighted Dirichlet spaces that are power bounded, Ces\`{a}ro bounded and uniformly Kreiss. Moreover, we show the equivalence in such spaces between mean ergodicity and Ces\`{a}ro…
In a recent survey paper we introduced one-sided multipliers between two different operator spaces. Here we give some basic theory for these maps.
The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
We consider fractional Schr\"odinger operators $H=(-\Delta)^\alpha+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2\alpha$, $\alpha>1$. We show that the wave operators extend to bounded operators on $L^p(\mathbb R^n)$ for…
This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m},…
We investigate some new classes of operator algebras which we call semi-$\sigma$-finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson's…
In this article we study the Ces\`{a}ro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$…
The paper gives the background for Toeplitz $T_a$ and Hankel $H_a$ operators acting between distinct Hardy type spaces over the unit circle $\mathbb{T}$. We characterize possible symbols of such operators and prove general versions of…
Let S be the set of scalings 1, 2,3,4, ... and consider the corresponding set of scaled lattices in the plane. In this paper averaging operators are defined for plaquette functions on a lattice to plaquette functions on a coarser lattice…
This paper showed that fractional p-adic Hardy operator norms in p-adic Herz-Morrey spaces with varying exponents are bounded. Corresponding commutator operators are also estimated for p-adic variable central bounded mean oscillations…
We survey results concerning the spectral properties of limit-periodic operators. The main focus is on discrete one-dimensional Schr\"odinger operators, but other classes of operators, such as Jacobi and CMV matrices, continuum…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We relate the existence and regularity of a solution operator to on smoothly bounded pseudoconvex domains to the existence and regularity of a projection operator onto the kernel of dbar.