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Fundamental solutions for Dirac-type operators

Swanhild Bernstein (1996)

Banach Center Publications

We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces C 1 ( G ) and W p 1 ( G ) . Further, we consider the Cauchy problem for this operator.

Further convergence results for two quadrature rules for Cauchy type principal value integrals

Nikolaos I. Ioakimidis (1982)

Aplikace matematiky

New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to 1 2 . The results obtained here supplement...

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