On a functional equation arising in the kinetic theory of gases

Leif Arkeryd; Carlo Cercignani

Displaying similar documents to “On a functional equation arising in the kinetic theory of gases”

A problem with almost everywhere equality

Piotr Niemiec (2012)

Annales Polonici Mathematici

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A topological space Y is said to have (AEEP) if the following condition is satisfied: Whenever (X,) is a measurable space and f,g: X → Y are two measurable functions, then the set Δ(f,g) = x ∈ X: f(x) = g(x) is a member of . It is shown that a metrizable space Y has (AEEP) iff the cardinality of Y is not greater than $2^{ℵ ₀}$ .

A Lipschitzian characterization of approximately differentiable functions

Austin, D.G. (1956)

Portugaliae mathematica

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Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Michel Talagrand (1982)

Annales de l'institut Fourier

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Let $G$ be a locally compact group. Let $L_{t}$ be the left translation in $L^{\infty} (G)$ , given by $L_{t} f (x) = f (t x)$ . We characterize (undre a mild set-theoretical hypothesis) the functions $f \in L^{\infty} (G)$ such that the map $t \to L_{t} f$ from $G$ into $L^{\infty} (G)$ is scalarly measurable (i.e. for $φ \in L^{\infty} (G)^{*}$ , $t \to φ (L_{t} f)$ is measurable). We show that it is the case when $t \to θ (L_{f} t)$ is measurable for each character $θ$ , and if $G$ is compact, if and only if $f$ is Riemann-measurable. We show that $t \to L_{t} f$ is Borel measurable if and only if $f$ is left uniformly continuous. Some of the measure-theoretic...

The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation

Janusz Brzdęk (1996)

Annales Polonici Mathematici

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Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation $f (x + f {(x)}^{n} y) = f (x) f (y)$ , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.

Asymptotic equivalence between two systems of ordinary differential equations

Onuchic, Nelson (1971)

Portugaliae mathematica

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Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

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In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.

Measurable solutions of functional equations satisfied almost everywhere.

Járai, Antal (1999)

Mathematica Pannonica

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Angular limits of the integrals of the Cauchy type

Josef Král, Dagmar Medková (1997)

Czechoslovak Mathematical Journal

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Integrals of the Cauchy type extended over the boundary $\partial A$ of a general compact set $A$ in the complex plane are investigated. Necessary and sufficient conditions on $\partial A$ are established guaranteeing the existence of angular limits of these integrals at a fixed $z \in \partial A$ for all densities satisfying a Hölder-type condition at $z$ .