### ... and Schrödinger operators.

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We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions...

Si considera l’equazione astratta $B{A}_{1}u+{A}_{0}u=h$, dove ${A}_{i}$$(i=\mathrm{0...A\; note\; on\; the\; Rellich\; formula\; in\; Lipschitz\; domains.Alano\; Ancona\; (1998)Publicacions\; Matem\xe0tiquesLet\; L\; be\; a\; symmetric\; second\; order\; uniformly\; elliptic\; operator\; in\; divergence\; form\; acting\; in\; a\; bounded\; Lipschitz\; domain\; \xad\Omega \; of\; RN\; and\; having\; Lipschitz\; coefficients\; in\; \Omega \xad.\; It\; is\; shown\; that\; the\; Rellich\; formula\; with\; respect\; to\; \Omega \xad\; and\; L\; extends\; to\; all\; functions\; in\; the\; domain\; D\; =\; \{u\; \in \; H01(\Omega \xad);\; L(u)\; \in \; L2(\xad\Omega )\}\; of\; L.\; This\; answers\; a\; question\; of\; A.\; Cha\xefra\; and\; G.\; Lebeau.A\; Paley-Wiener\; type\; theorem\; for\; generalized\; non-quasianalytic\; classesJordi\; Juan-Huguet\; (2012)Studia\; MathematicaLet\; P\; be\; a\; hypoelliptic\; polynomial.\; We\; consider\; classes\; of\; ultradifferentiable\; functions\; with\; respect\; to\; the\; iterates\; of\; the\; partial\; differential\; operator\; P(D)\; and\; prove\; that\; such\; classes\; satisfy\; a\; Paley-Wiener\; type\; theorem.\; These\; classes\; and\; the\; corresponding\; test\; spaces\; are\; nuclear.A\; partial\; differential\; operator\; which\; is\; surjective\; on\; Gevrey\; classes$ {\Gamma}^{d}\left(\mathbb{R}\xb3\right)$with\; 1\; \le \; d\; <\; 2\; and\; d\; \ge \; 6\; but\; not\; for\; 2\; \le \; d\; <\; 6R\xfcdiger\; Braun\; (1993)Studia\; MathematicaIt\; is\; shown\; that\; the\; partial\; differential\; operator$ P\left(D\right)=\partial \u2074/\partial x\u2074-\partial \xb2/\partial y\xb2+i\partial /\partial z:{\Gamma}^{d}\left(\mathbb{R}\xb3\right)\to {\Gamma}^{d}\left(\mathbb{R}\xb3\right)$is\; surjective\; if\; 1\; \le \; d\; <\; 2\; or\; d\; \ge \; 6\; and\; not\; surjective\; for\; 2\; \le \; d\; <\; 6.A\; remark\; on\; the\; differential\; equations\; on\; the\; sphereAlois\; \u0160vec\; (1976)\u010casopis\; pro\; p\u011bstov\xe1n\xed\; matematikyA\; result\; on\; the\; well\; posedness\; of\; the\; Cauchy\; problem\; for\; a\; class\; of\; hyperbolic\; operators\; with\; double\; characteristicsMilena\; Petrini\; (1995)Rendiconti\; del\; Seminario\; Matematico\; della\; Universit\xe0\; di\; PadovaA\; semilinear\; equation\; in$ {L}^{1}\left({\mathbb{R}}^{N}\right)$Philippe\; Benilan,\; Haim\; Brezis,\; Michael\; G.\; Crandall\; (1975)Annali\; della\; Scuola\; Normale\; Superiore\; di\; Pisa\; -\; Classe\; di\; ScienzeCurrently\; displaying\; 1\; \u2013\; 20\; of\; 498Page\; 1Next\$(document).ready(function()\; \{\; \$("\#tabs").tabs();\; \});EuDMLAbout\; EuDML\; initiativeFeedbackversion\; 2.1.7}$