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Differentiable bundles of subspaces and operators in Banach spaces

Frank Mantlik — 1991

Studia Mathematica

Isomorphic classification and lifting theorems for spaces of differentiable functions with Lipschitz conditions

Frank Mantlik — 1991

Studia Mathematica

Partial differential operators depending analytically on a parameter

Frank Mantlik — 1991

Annales de l'institut Fourier

Let $P (λ, D) = \sum_{| α | \leq m} a_{α} (λ) D^{α}$ be a differential operator with constant coefficients $a_{α}$ depending analytically on a parameter $λ$ . Assume that the family ${$ P( $λ$ ,D) $}$ is of constant strength. We investigate the equation $P (λ, D) 𝔣_{λ} \equiv g_{λ}$ where $𝔤_{λ}$ is a given analytic function of $λ$ with values in some space of distributions and the solution $𝔣_{λ}$ is required to depend analytically on $λ$ , too. As a special case we obtain a regular fundamental solution of P( $λ$ ,D) which depends analytically on $λ$ . This result answers a question of L. Hörmander.

Note on the absolutely continuous spectrum of Sturm-Liouville operators.

Albert Schneider; Frank Mantlik — 1990

Mathematische Zeitschrift

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Currently displaying 1 – 4 of 4

Differentiable bundles of subspaces and operators in Banach spaces

Isomorphic classification and lifting theorems for spaces of differentiable functions with Lipschitz conditions

Partial differential operators depending analytically on a parameter

Note on the absolutely continuous spectrum of Sturm-Liouville operators.