Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch

Displaying similar documents to “Localizations of partial differential operators and surjectivity on real analytic functions”

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Solving a problem of L. Schwartz, those constant coefficient partial differential operators $P (D)$ are characterized that admit a continuous linear right inverse on $ℰ (Ω)$ or $𝒟^{'} (Ω)$ , $Ω$ an open set in $R^{n}$ . For bounded $Ω$ with $C^{1}$ -boundary these properties are equivalent to $P (D)$ being very hyperbolic. For $Ω = R^{n}$ they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial $P$ .

Analytic formulas for the hyperbolic distance between two contractions

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In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes...

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