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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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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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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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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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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
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Systems of functional equations
Random Structures & Algorithms, 2000In this paper ``functional equation'' is an equation of particular form from which an implicit unknown function is to be determined. To be exact, the author looks for analytic solutions (complex variables are written in italics, vector variables and vector valued functions with \(n\) complex components are set in bold face) \({\mathbf y}={\mathbf g}(x,{
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On a Functional Differential Equation
IMA Journal of Applied Mathematics, 1971Fox, L. +3 more
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DoFun 3.0: Functional equations in mathematica
Computer Physics Communications, 2020Markus Q Huber +2 more
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