Related papers: A note on rational numbers and certain operators
We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
We scrutinize the possibility of extending the result of \cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two…
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…
The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at infinity and the resultant.
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of…
In this paper, we introduce the higher order generalization of Bernstein type operators defined by (p,q)-integers. We establish some approximation results for these new operators by using the modulus of continuity.
In this paper, we present new characterizations of normal and positive operators in terms of their powers. Among other things, we show that if $T^2$ is normal, $\mathcal{W}(T^{2k+1})$ lies on one side of a line passing through the origin…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a "$q$-analogue of a real." The construction is based on the notion of $q$-deformed rational number introduced in…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
In the present paper, we establish a general transformation for $q$-series which contains L. Wang et al's transformation involved in Nahm series. As direct applications, some concrete new transformation formulas for the ${}_{r+1}\phi_r$…
We prove a pointwise estimate for positive dyadic shifts of complexity $m$ which is linear in the complexity. This can be used to give a pointwise estimate for Calder\'on-Zygmund operators and to answer a question posed by A. Lerner.…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…