Download Functional Analysis and Complex Analysis: September 17-21, by Aydin Aytuna, Reinhold Meise, Tosun Terzioglu, Dietmar Vogt PDF

By Aydin Aytuna, Reinhold Meise, Tosun Terzioglu, Dietmar Vogt

ISBN-10: 0821844601

ISBN-13: 9780821844601

In recent times, the interaction among the tools of useful research and intricate research has ended in a few outstanding leads to a wide selection of issues. It grew to become out that the constitution of areas of holomorphic services is essentially associated with definite invariants in the beginning outlined on summary Frechet areas in addition to to the advancements in pluripotential conception. the purpose of this quantity is to rfile the various unique contributions to this subject awarded at a convention held at Sabanci college in Istanbul, in September 2007. This quantity additionally includes a few surveys that provide an outline of the cutting-edge and begin extra learn within the interaction among practical and intricate research

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Extra info for Functional Analysis and Complex Analysis: September 17-21, 2007, Sabanci University, Istanbul, Turkey

Example text

10. Proposition. Let ω be a weight function and let Tµ = 0 be an {ω}ultradifferential operator. If the Fourier-Laplace transform µ ˆ of µ is {ω}-slowly decreasing, then for each a, b ∈ R with a < b the following assertions hold: (1) ker Tµ,[a,b] is isomorphic to Λ0 (γ)b , where γ = (ω(aj ))j∈N and where (aj )j∈N counts the zeros of µ ˆ with multiplicities in such a way that (ω(aj ))j∈N is increasing. (2) If lim|z|→∞,z∈V (ˆµ) | Im(z)|/ω(z) = 0 then the map [a,b] : ker Tµ → ker Tµ,[a,b] , [a,b] (f ) := f |[a,b] , is an isomorphism.

References [1] J. Bonet, P. Domanski: Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences, J. Funct. Analysis 230 (2006), 329–381. [2] J. Bonet, A. Galbis, R. Meise: On the range of convolution operators on non-quasianalytic ultradifferentiable functions, Studia Math. 126 (1997), 171–198. [3] J. Bonet, A. Galbis, S. Momm: Nonradial H¨ ormander algebras of several variables and convolution operators, Trans. Amer. Math. Soc.

110 (1994), 65–82. [15] R. Meise: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals, J. reine angew. Math. 363 (1985), 59–95. [16] R. Meise: Sequence spaces representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type, Studia Math. 92 (1989), 211–230. [17] R. Meise, B. A. Taylor: A decomposition lemma for entire functions and its applications to spaces of ultradifferentiable functions, Math. Nachr. 142 (1989), 45–72.

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