Abstract
We prove that the Hermite functions are an absolute Schauder basis for many weighted spaces of (ultra)differentiable functions and ultradistributions including the space of Fourier hyperfunctions. The coefficient spaces are also determined.
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References
Gelfand, I.M., Shilov, G.E.: Generalized functions. Vol. 2, Academic Press, New York/London, 1968
Kaneko, A.: Introduction to hyperfunctions.Kluwer, Dordrecht/Boston, 1988
Langenbruch, M.: Ultradifferentiable functions on compact intervals. Math. Nachr. 140, 109–126 (1989)
Langenbruch, M.: Surjectivity of partial differential operators. Note di Mat. Vol. X (Suppl. n. 2), 369–388 (1990)
Langenbruch, M.: Convolution operators on Fourier hyperfunctions. Preprint
Langenbruch, M.: Right inverses for partial differential operators on Fourier hyperfunctions. Manuscript
Meise, R., Vogt, D.: Introduction to functional analysis. Clarendon Press, Oxford, 1997
Roumieu, C.: Ultra-distributions definies sur ℝn et sur certains classes des varietes differentiables. J. Analyse Math. 10, 153–192 (1962-63)
Sato, M.: Theory of hyperfunctions (in Japanese). Sugaku 10, 1–27 (1958)
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Dedicated to Professor H.-G. Tillmann on the occasion of his 80th birthday
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Langenbruch, M. Hermite functions and weighted spaces of generalized functions. manuscripta math. 119, 269–285 (2006). https://doi.org/10.1007/s00229-005-0605-y
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DOI: https://doi.org/10.1007/s00229-005-0605-y