The Characterization of the Cylinder Functions by a Functional Equation

1975 ◽  
Vol 6 (3) ◽  
pp. 488-495 ◽  
Author(s):  
A. McD. Mercer
Keyword(s):  
Functional Equation

scholarly journals Some results concerning the Cauchy functional equation in certain Banach algebras

1985 ◽  
Vol 31 (1) ◽  
pp. 137-144 ◽  
Author(s):  
J. Vukman
Keyword(s):  
Functional Equation ◽  
Hilbert Space ◽  
Identity Element ◽  
Banach Algebras ◽  
Cauchy Functional Equation

In this paper some results concerning the Cauchy functional equation, that is the functional equation f(x+y) = f(x) + f(y) in complex hermitian Banach *-algebras with an identity element are presented. As an application a generalization of Kurepa's extension of the Jordan-Neumann characterization of pre-Hilbert space is obtained.

Lifetime regression models based on a functional equation of physical nature

1987 ◽  
Vol 24 (01) ◽  
pp. 160-169 ◽  
Author(s):  
Enrique Castillo ◽  
Janos Galambos
Keyword(s):  
Functional Equation ◽  
Conditional Distribution ◽  
Regression Models ◽  
Practical Problem ◽  
Ad Hoc ◽  
Physical Nature ◽  
Value Theory ◽  
Complete Characterization ◽  
Lifetime Data

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

scholarly journals On the general solution of a functional equation connected to sum form information measures on open domain—III

1986 ◽  
Vol 9 (3) ◽  
pp. 545-550 ◽  
Author(s):  
Pl. Kannappan ◽  
P. K. Sahoo
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Open Domain ◽  
Information Measures ◽  
Domain Iii ◽  
Weighted Entropy ◽  
Form Information

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degreeβ. Here, we find the general solution of the functional equation (2) on an open domain, without using0-probability and1-probability.

scholarly journals A functional equation related to generalized entropies and the modular group

2020 ◽  
Vol 94 (6) ◽  
pp. 1201-1212
Author(s):  
Daniel Bennequin ◽  
Juan Pablo Vigneaux
Keyword(s):  
Functional Equation ◽  
Modular Group ◽  
General Relation ◽  
Algebraic Characterization ◽  
Conditional Probabilities ◽  
Related System ◽  
System Of Functional Equations ◽  
Symmetry Of The Solution ◽  
Generalized Entropies

Abstract We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies. These transformations generate the modular group, and this fact plays a crucial role in solving the system. The method suggests a more general relation between conditional probabilities and arithmetic.

scholarly journals On a generalization of Hamburger’s theorem

1985 ◽  
Vol 98 ◽  
pp. 67-76 ◽  
Author(s):  
Akinori Yoshimoto
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Summation Formula ◽  
Number Fields ◽  
Gaussian Field ◽  
Algebraic Number Fields ◽  
Ring Of Integers ◽  
Poisson’S Summation Formula ◽  
The Relationship

The relationship between Poisson’s summation formula and Hamburger’s theorem [2] which is a characterization of Riemann’s zetafunction by the functional equation was already mentioned in Ehrenpreis-Kawai [1]. There Poisson’s summation formula was obtained by the functional equation of Riemann’s zetafunction. This procedure is another proof of Hamburger’s theorem. Being interpreted in this way, Hamburger’s theorem admits various interesting generalizations, one of which is to derive, from the functional equations of the zetafunctions with Grössencharacters of the Gaussian field, Poisson’s summation formula corresponding to its ring of integers [1], The main purpose of the present paper is to give a generalization of Hamburger’s theorem to some zetafunctions with Grössencharacters in algebraic number fields. More precisely, we first define the zetafunctions with Grössencharacters corresponding to a lattice in a vector space, and show that Poisson’s summation formula yields the functional equations of them. Next, we derive Poisson’s summation formula corresponding to the lattice from the functional equations.

Sign in / Sign up

Export Citation Format

Share Document