On iterations of non-negative operators and their applications to elliptic systems

Описание

Тип публикации: статья из журнала

Год издания: 2000

Ключевые слова: elliptic systems; Cauchy problem

Аннотация: Let H-0, H-1 be Hilbert spaces and L: H-0 - H-1 be a linear bounded operator with \\L\\ less than or equal to 1 Then L* L is a bounded linear self-adjoint non-negative operator in the Hilbert space Ho and one can use the Neumann series Sigma (infinity)(nu =o)(I - L* L)L-nu* f in order to study solvability of the operator equation LПоказать полностьюu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral.

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Издание

Журнал: MATHEMATISCHE NACHRICHTEN

Выпуск журнала: Vol. 218

Номера страниц: 165-174

ISSN журнала: 0025584X

Место издания: BERLIN

Издатель: WILEY-V C H VERLAG GMBH

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