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On Iterations of Non–Negative Operators and Their Applications to Elliptic Systems

✍ Scribed by Alexander Shlapunov

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 172 KB
Volume: 218
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200010)218:1<165::aid-mana165>3.0.co;2-w

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✦ Synopsis

H 0 and one can use the Neumann series ∞ ν=0 (I -L L) ν L f in order to study solvability of the operator equation Lu = f .

In particular, applying this method to the ill -posed Cauchy problem for solutions to an elliptic system P u = 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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