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ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS
Mathematics of the USSR-Izvestiya, 1967The paper adduces a theorem of a general form on functional equations of the Dirichlet functions, as well as certain of its corollaries.
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Mathematics of the USSR-Izvestiya, 1978
Necessary and sufficient conditions are found for the existence and uniqueness of local solutions of multidimensional linear functional equations of the form . Sufficient conditions for local solvability are also obtained for equations with variable coefficients.Bibliography: 5 titles.
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Necessary and sufficient conditions are found for the existence and uniqueness of local solutions of multidimensional linear functional equations of the form . Sufficient conditions for local solvability are also obtained for equations with variable coefficients.Bibliography: 5 titles.
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On the Robustness of Functional Equations
SIAM Journal on Computing, 1999Summary: We study the general question of how characteristics of functional equations influence whether or not they are robust. We isolate examples of properties which are necessary for the functional equations to be robust. On the other hand, we show other properties which are sufficient for robustness.
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On Fréchet’s functional equation
Monatshefte für Mathematik, 2013The paper is devoted to the basic theorem on polynomials, originally proved by \textit{D. Ž. Đoković} [Ann. Pol. Math. 22, 189--198 (1969; Zbl 0187.39903)], which states that a function \(f: G\to\mathbb{C}\), defined on an abelian group \(G\), is a generalized polynomial of degree at most \(n\), i.e., satisfies Fréchet's equation \[ \Delta_{y_1,y_2 ...
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On a Multilinear Functional Equation
Mathematical Notes, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On A Functional Equation of Abel
Results in Mathematics, 1994The authors determine the general solution of \(\psi (x + y) = g(xy) + h(x - y)\), for \(\psi, g,h : K \to G\), where \(K\) is a field and \(G\) is an Abelian group, which was first treated by Abel in his 1823 manuscript.
Chung, J. K. +4 more
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A Functional Equation For Implication
The Mathematical Gazette, 1967Since all truth functions in two-valued logic may be represented by polynomials in the arithmetic of residues modulo 2, the question which R. Sibson raises in note 3127 may be expressed in the following form : Find all polynomials Φ(p, q) such that identically, where p & q is a commutative polynomial which vanishes only when p = q = 0, and p & ...
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A Functional Equation for the Cosine
Canadian Mathematical Bulletin, 1968It is known [3], [5] that, the complex-valued solutions of(B)(apart from the trivial solution f(x)≡0) are of the form(C)(D)In case f is a measurable solution of (B), then f is continuous [2], [3] and the corresponding ϕ in (C) is also continuous and ϕ is of the form [1],(E)In this paper, the functional equation(P)where f is a complex-valued, measurable
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The semiclassical functional equation
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1992A semiclassical analog of the functional equation for the Riemann zeta function is considered. In the case of the zeta function itself, this equation forms the basis for a finite approximation to the Dirichlet series, known as the approximate functional equation.
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A Note on a Functional Equation
American Journal of Mathematics, 1951and determine the conditions on a polynomial F (x, y) in order that (1) can have a continuous strictly monotone (say increasing) solution. If F(x, y) is x + y or xy, we have the classical cases of Cauchy's functional equations. The cases when F(x, y) is a general linear function,1 and also the case when it is x + y + nxy, have been treated.2 In this ...
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