On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations
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DOI: 10.1007/s00010-017-0490-y
Abstract: The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions… read more here.
Keywords: inhomogeneous linear; functional equations; spectral analysis; linear functional ... See more keywords
On Fermat Diophantine functional equations, little Picard theorem and beyond
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DOI: 10.1007/s00010-018-0614-z
Abstract: We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$fm(z)+gn(z)=1 with integers $$m,n\ge 2$$m,n≥2, from which other approaches to proving the little Picard theorem are discussed. read more here.
Keywords: picard theorem; diophantine functional; functional equations; little picard ... See more keywords
Nice results about quadratic type functional equations on semigroups
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DOI: 10.1007/s00010-019-00653-w
Abstract: Let $$(S,+)$$ ( S , + ) be an abelian semigroup, let $$\sigma $$ σ be an involution of S , let X be a linear space over the field $${\mathbb {K}}\in \{{\mathbb {R}},{\mathbb {C}}\}$$… read more here.
Keywords: quadratic type; nice results; results quadratic; functional equations ... See more keywords
Some generalized quadratic functional equations on monoids
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DOI: 10.1007/s00010-019-00690-5
Abstract: We solve two Pexiderized extensions of the quadratic functional equation on monoids. The equation is extended by replacing the group inversion in the classical quadratic equation with an involution, which may be either homomorphic or… read more here.
Keywords: equations monoids; functional equations; quadratic functional; generalized quadratic ... See more keywords
On a new class of functional equations satisfied by polynomial functions
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DOI: 10.1007/s00010-021-00781-2
Abstract: The classical result of L. Szekelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Szekelyhidi’s result may be generalized to equations where… read more here.
Keywords: equations satisfied; class functional; satisfied polynomial; new class ... See more keywords
An Application of Medial Limits to Iterative Functional Equations
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DOI: 10.1007/s00025-020-01229-w
Abstract: Assume that $$(\Omega ,{\mathcal {A}},P)$$ ( Ω , A , P ) is a probability space, $$f:[0,1]\times \Omega \rightarrow [0,1]$$ f : [ 0 , 1 ] × Ω → [ 0 , 1 ]… read more here.
Keywords: application medial; omega omega; functional equations; limits iterative ... See more keywords
Levi-Civita functional equations and the status of spectral synthesis on semigroups
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DOI: 10.1007/s00233-021-10211-z
Abstract: We show, contrary to some published statements, that spectral synthesis does not generally hold for commutative semigroups that are not groups. On the positive side we prove that it holds if the semigroup is a… read more here.
Keywords: synthesis; semigroups prime; spectral synthesis; civita functional ... See more keywords
Alienation of the Quadratic And Additive Functional Equations
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DOI: 10.1007/s10476-019-0869-1
Abstract: Let G, H be uniquely 2-divisible Abelian groups. We study the solutions f, g: G → H of Pexider type functional equation (*)$$f(x+y)+f(x-y)+g(x+y)=2f(x)+2f(y)+g(x)+g(y),$$f(x+y)+f(x−y)+g(x+y)=2f(x)+2f(y)+g(x)+g(y), resulting from summing up the well known quadratic functional equation and additive… read more here.
Keywords: quadratic additive; alienation quadratic; additive functional; equation ... See more keywords
Almost Periodic Solutions of Functional Equations
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DOI: 10.1007/s10958-017-3305-8
Abstract: We establish conditions for the existence of almost periodic solutions of linear and nonlinear almost periodic functional equations without using the -classes of these equations. read more here.
Keywords: almost periodic; functional equations; periodic solutions; solutions functional ... See more keywords
Functional Equations and Identification Problems
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DOI: 10.1007/s10958-020-04776-3
Abstract: We consider identification problems and connections of such problems with linear functional equations. The results are applied to the study of solutions to evolution equations and Navier–Stokes equations. read more here.
Keywords: identification problems; functional equations; equations identification;
Linear Functional Equations with 𝔇H-Unstable Solutions
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DOI: 10.1007/s10958-021-05228-2
Abstract: We establish conditions for the absolute instability of solutions of linear functional equations with self-adjoint operator coefficients. read more here.
Keywords: equations unstable; unstable solutions; linear functional; solutions linear ... See more keywords