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An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions

J. Cichoń, Michał Morayne (1993)

Fundamenta Mathematicae

We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...

An algebraic derivative associated to the operator D δ

V. Almeida, N. Castro, J. Rodríguez (2000)

Banach Center Publications

In this paper we get an algebraic derivative relative to the convolution ( f * g ) ( t ) = ∫ 0 t i f ( t - ψ ) g ( ψ ) d ψ associated to the operator D δ , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Kilbas, Anatoly, Repin, Oleg (2010)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...

An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

Frank Oertel (2015)

Dependence Modeling

We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.

An analysis of the stability boundary for a linear fractional difference system

Tomáš Kisela (2015)

Mathematica Bohemica

This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference...

An axiomatic theory of non-absolutely convergent integrals in Rn

W. Jurkat, D. Nonnenmacher (1994)

Fundamenta Mathematicae

We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.

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