Related papers: Multi-parameter singular integral operators and re…
We give new a proof of the general Brian\c{c}on-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a…
We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solve the analogous…
We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…
This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…
We generalize Menon's identity by considering sums representing arithmetical functions of several variables. As an application, we give a formula for the number of cyclic subgroups of the direct product of several cyclic groups of arbitrary…
A fundamental problem from invariant theory is to describe the endomorphism algebra of multilinear functions on a representation V invariant under the action of a group G. According to Weyl's classic, a first main (later: fundamental)…
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it satisfies a…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…
Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of…
In the article integer divisibility properties and related prime factors natural number representation concepts have been defined over the whole infinite hyperoperation hierarchy. The definitions have been made across and above of unique…
We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions,…
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration. Under the condition (A), we get an integral representation formula for the…
In this paper we construct examples of commutative rings of difference operators with matrix coefficients from representation theory of quantum groups, generalizing the results of our previous paper to the $q$-deformed case. A generalized…
We give again a proof of non-homogeneous T1 theorem. Our proof consists of three main parts: a construction of a random dyadic lattice; an estimate of matrix coefficients of a Calder\'on--Zygmund operator with respect to random Haar basis…