Abstract
We provide a projective description for a class of generalized Gelfand–Shilov spaces of Roumieu type. In particular, our results apply to the classical Gelfand–Shilov spaces and weighted L ∞-spaces of ultradifferentiable functions of Roumieu type.
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References
F. Bastin, On bornological \(C\overline {V}(X)\) spaces. Arch. Math. 53, 394–398 (1989)
C.A. Berenstein, M.A. Dostal, Analytically Uniform Spaces and Their Applications to Convolution Equations. Lecture notes in mathematics, vol. 256 (Springer, Berlin, 1972)
K.D. Bierstedt, R. Meise, W.H. Summers, A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272, 107–160 (1982)
A. Debrouwere, J. Vindas, On weighted inductive limits of spaces of ultradifferentiable functions and their duals. Math Nachr. (in press). https://doi.org/10.1002/mana.201700395
A. Debrouwere, J. Vindas, Solution to the first Cousin problem for vector-valued quasianalytic functions. Ann. Mat. Pura Appl. 196, 1983–2003 (2017)
A. Debrouwere, J. Vindas, On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Math. RACSAM 112, 473–508 (2018)
A. Debrouwere, H. Vernaeve, J. Vindas, Optimal embeddings of ultradistributions into differential algebras. Monatsh. Math. 186(3), 407–438 (2018)
P. Dimovski, B. Prangoski, J. Vindas, On a class of translation-invariant spaces of quasianalytic ultradistributions. Novi Sad J. Math. 45, 143–175 (2015)
L. Ehrenpreis, Fourier Analysis in Several Complex Variables (Wiley, New York, 1970)
K. Gröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, Boston, 2001)
H. Komatsu, Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Tokyo IA Math. 20, 25–105 (1973)
H. Komatsu, Ultradistributions III. Vector valued ultradistributions and the theory of kernels. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29, 653–717 (1982)
S. Pilipović, Characterization of bounded sets in spaces of ultradistributions. Proc. Am. Math. Soc. 120, 1191–1206 (1994)
S. Pilipović, B. Prangoski, J. Vindas, On quasianalytic classes of Gelfand–Shilov type. Parametrix and convolution. J. Math. Pures Appl. 116, 174–210 (2018)
B. Prangoski, Laplace transform in spaces of ultradistributions. Filomat 27, 747–760 (2013)
Acknowledgements
A. Debrouwere acknowledges support by FWO-Vlaanderen, through the postdoctoral grant 12T0519N. The work of J. Vindas was supported by Ghent University, through the BOF-grants 01N01014 and 01J04017.
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Debrouwere, A., Vindas, J. (2019). A Projective Description of Generalized Gelfand–Shilov Spaces of Roumieu Type. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_39
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DOI: https://doi.org/10.1007/978-3-030-04459-6_39
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