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

• Autorzy: W. B. Jurkat , D. J. F. Nonnenmacher
• Języki publikacji: EN

Abstrakty

EN

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in $ℝ^n$, we are led to an integration process over quite general sets $A ⊆ q ℝ^n$ 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.

Kategorie tematyczne

• 26B20: Integral formulas (Stokes, Gauss, Green, etc.)
• 26A39: Denjoy and Perron integrals, other special integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 1
• Strony: 69-84

Daty

wydano

1994

otrzymano

1993-08-24

Twórcy

autor

W. B. Jurkat

• Abteilung Mathematik II und V, Universität Ulm, D-89069 Ulm, Germany

autor

D. J. F. Nonnenmacher

• Abteilung Mathematik II und V, Universität Ulm, D-89069 Ulm, Germany

Bibliografia

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• [Jar-Ku 2] J. Jarník and J. Kurzweil, A non-absolutely convergent integral which admits transformation and can be used for integration on manifolds, Czechoslovak Math. J. 35 (110) (1985), 116-139.
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• [Ju-No 1] W. B. Jurkat and D. J. F. Nonnenmacher, An axiomatic theory of non-absolutely convergent integrals in $ℝ^n$, Fund. Math. 145 (1994), 221-242.
• [Ju-No 2] W. B. Jurkat and D. J. F. Nonnenmacher, A generalized n-dimensional Riemann integral and the Divergence Theorem with singularities, Acta Sci. Math. (Szeged) 59 (1994), 241-256.
• [Ju-No 3] W. B. Jurkat and D. J. F. Nonnenmacher, The Fundamental Theorem for the $ν_1$-integral on more general sets and a corresponding Divergence Theorem with singularities, Czechoslovak Math. J., to appear.
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• [No 1] D. J. F. Nonnenmacher, Sets of finite perimeter and the Gauss-Green Theorem with singularities, J. London Math. Soc., to appear.
• [No 2] D. J. F. Nonnenmacher, A constructive definition of the n-dimensional ν(S)-integral in terms of Riemann sums, preprint 1992, to appear.
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• [Pf 2] W. F. Pfeffer, The Gauss-Green Theorem, Adv. in Math. 87 (1991), 93-147.