Search results for "Function"

Extension maps in ultradifferentiable and ultraholomorphic function spaces

2000

Representations of Certain Banach C*-modules

2004

The possibility of extending the well known Gelfand–Naimark– Segal representation of *-algebras to certain Banach C*-modules is studied. For this aim the notion of modular biweight on a Banach C*-module is introduced. For the particular class of strict pre CQ*-algebras, two different types of representations are investigated.

Functional Derivative Approach

2001

Let us now leave the path integral formalism temporarily and reformulate operatorial quantum mechanics in a way which will make it easy later on to establish the formal connection between operator and path integral formalism. Our objective is to introduce the generating functional into quantum mechanics. Naturally we want to generate transition amplitudes. The problem confronting us is how to transcribe operator quantum mechanics as expressed in Heisenberg’s equation of motion into a theory formulated solely in terms of c-numbers. This can be achieved either by Schwinger’s action principle or with the aid of a generation functional defined as follows:

On difference of operators with different basis functions

2019

In the recent years several researchers have studied problems concerning the difference of two linear positive operators, but all the available literature on this topic is for operators having same basis functions. In the present paper, we deal with the general quantitative estimate for the difference of operators having different basis functions. In the end we provide some examples. The estimates for the differences of two operators can be obtained also using classical result of Shisha and Mond. Using numerical examples we will show that for particular cases our result improves the classical one.

Dynamics of differentiation and integration operators on weighted spaces of entire functions

2014

On Inductive Generalization in Monadic First-Order Logic With Identity

1966

Publisher Summary The chapter examines the results obtained by means of a system when the relation of identity is used in addition to monadic predicates. The chapter compares the new system of inductive logic sketched by Jaakko Hintikka with Carnap's system. The main advantage of Hintikka's system is that it gives natural degrees of confirmation to inductive generalizations, whereas Carnap's confirmation function c * enables one to deal satisfactorily with singular inductive inference only. According to Carnap's system, general sentences that are not logically true receive nonnegligible degrees of confirmation only if the evidence contains a large part of the individuals in the whole univer…

Some problems in number theory that arise from group theory

2021

In this expository paper, we present several open problems in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.

Continuity of solutions of linear, degenerate elliptic equations

2009

We consider the simplest form of a second order, linear, degenerate, divergence structure equation in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

A note on multiple summing operators and applications

2018

We prove a new result on multiple summing operators and, among other results and applications, we provide a new extension of Littlewood’s 4 / 3 inequality to m-linear forms.

Product of extension domains is still an extension domain

2018

We prove the product of the Sobolev-extension domains is still a Sobolev-extension domain.