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We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak $*$ spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.

Characterizations of those Ideals in L1 (R) which can be Synthesized.

Carl L. DeVito (1973)

Mathematische Annalen

Contractions à spectre dénombrable et propriétés d'unicité des fermés dénombrables du cercle

Mohamed Zarrabi (1993)

Annales de l'institut Fourier

On montre que si $T$ est une contraction à spectre dénombrable et telle que, pour tout $ϵ > 0$ $∥ T^{- 1} ...$

D'Alembert's functional equation on compact groups.

Székelyhidi, László (2007)

Banach Journal of Mathematical Analysis [electronic only]

Das Syntheseproblem für invariante Distributionen.

R. Felix (1981/1982)

Inventiones mathematicae

Discrete spectral synthesis.

Székelyhidi, László (2005)

Annales Mathematicae et Informaticae

Ditkin sets in homogeneous spaces

Krishnan Parthasarathy, Nageswaran Shravan Kumar (2011)

Studia Mathematica

Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.

Ditkin's Condition and Primary Ideals in Central Beurling Algebras.

Richard D. Mosak (1978)

Monatshefte für Mathematik

Ditkin's Theorem and ...SIN...-Groups.

Bruce A. Barnes (1983)

Monatshefte für Mathematik

Ensemble de non-synthèse uniforme dans les algèbres $A_{p} (G)$

N. Lohoue (1970)

Studia Mathematica

Ensembles de non synthèse pour certains poids dissymétriques sur la droite

M. Zarrabi (1993)

Studia Mathematica

Exponential monomials on Sturm-Liouville hypergroups.

Vajday, L. (2010)

Banach Journal of Mathematical Analysis [electronic only]

Faltungsoperatoren auf gewissen diskreten Gruppen

Michael Leinert (1974)

Studia Mathematica

Functional calculus in weighted group algebras.

Jacek Dziubanski, Jean Ludwig, Carine Molitor-Braun (2004)

Revista Matemática Complutense

Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G,ω). This functional calculus is then used to study harmonic analysis properties of L1(G,ω), such as the Wiener property and Domar's theorem.

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