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A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis

Hongfen Yuan (2017)

Czechoslovak Mathematical Journal

Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.

A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

Dirk Jens F. Nonnenmacher (1994)

Annales Polonici Mathematici

Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.

A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

W. Jurkat, D. Nonnenmacher (1994)

Fundamenta Mathematicae

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in n , we are led to an integration process over quite general sets A q n with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.

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.

Convolution of radius functions on ℝ³

Konstanty Holly (1994)

Annales Polonici Mathematici

We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary...

Green's theorem from the viewpoint of applications

Alexander Ženíšek (1999)

Applications of Mathematics

Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces W 1 , p ( ) H 1 , p ( ) ( 1 p ...

Henstock-Kurzweil integral on BV sets

Jan Malý, Washek Frank Pfeffer (2016)

Mathematica Bohemica

The generalized Riemann integral of Pfeffer (1991) is defined on all bounded BV subsets of n , but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of σ -finite Hausdorff measure of codimension one. Imposing a stronger regularity condition on partitions of BV sets, we define a Riemann-type integral which satisfies the usual additivity condition and extends the integral of Pfeffer. The new integral is lipeomorphism-invariant and closed with respect to the formation...

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