Related papers: The Cesaro operator
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
In this paper, for $p>1$ and $s>1$, we give a complete description of the boundedness and compactness of a Ces\`aro-like operator from the Besov space $B_p$ into a Banach space $X$ between the mean Lipschitz space $\Lambda^s_{1/s}$ and the…
Unitary vertex operator algebras are introduced and studied. It is proved that most well-known rational vertex operator algebras are unitary. The classification of unitary vertex operator algebras with central charge c less than or equal to…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to…
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
In this paper we develop a general concept of Lax operators on algebraic curves introduced in [1]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the…
By H\"ormander's $L^2$-method, we study the operator $\alpha \partial^k \bar{\partial}^{k} + \beta \bar{\partial}^k +\gamma \partial^k + c$ for any order $k$ with $\alpha, \beta, \gamma \in \mathbb{R}$ such that $(\alpha, \beta, \gamma)…
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
In this paper we study boundedness and detailed spectral properties for the Ces\`aro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Ces\`aro-Hardy operators and their dual…
We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
The purpose of the present paper is to investigate on a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding…
Various notions of dissipativity type for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case $L^p$-dissipativity. Most of the results are due to the authors.
We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of…