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.
Журнал: MATHEMATISCHE NACHRICHTEN
Выпуск журнала: Vol. 218
Номера страниц: 165-174
ISSN журнала: 0025584X
Место издания: BERLIN
Издатель: WILEY-V C H VERLAG GMBH