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On weighted inductive limits of spaces of ultradifferentiable functions and their duals

(2019) MATHEMATISCHE NACHRICHTEN. 292(3). p.573-602
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Analytic combinatorics of the transfinite: A Tauberian approach
Abstract
In the first part of this paper we discuss the completeness of two general classes of weighted inductive limits of spaces of ultradifferentiable functions. In the second part we study their duals and characterize these spaces in terms of the growth of convolution averages of their elements. This characterization gives a canonical way to define a locally convex topology on these spaces and we give necessary and sufficient conditions for them to be ultrabornological. In particular, our results apply to spaces of convolutors for Gelfand–Shilov spaces.
Keywords
completeness of inductive limits, convolution Gelfand-Shilov spaces, short‐time Fourier transform, ultrabornological (PLS)‐spaces

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Chicago
Debrouwere, Andreas, and Jasson Vindas Diaz. 2019. “On Weighted Inductive Limits of Spaces of Ultradifferentiable Functions and Their Duals.” Mathematische Nachrichten 292 (3): 573–602.
APA
Debrouwere, A., & Vindas Diaz, J. (2019). On weighted inductive limits of spaces of ultradifferentiable functions and their duals. MATHEMATISCHE NACHRICHTEN, 292(3), 573–602.
Vancouver
1.
Debrouwere A, Vindas Diaz J. On weighted inductive limits of spaces of ultradifferentiable functions and their duals. MATHEMATISCHE NACHRICHTEN. 2019;292(3):573–602.
MLA
Debrouwere, Andreas, and Jasson Vindas Diaz. “On Weighted Inductive Limits of Spaces of Ultradifferentiable Functions and Their Duals.” MATHEMATISCHE NACHRICHTEN 292.3 (2019): 573–602. Print.
@article{8606703,
  abstract     = {In the first part of this paper we discuss the completeness of two general classes of weighted inductive limits of spaces of ultradifferentiable functions. In the second part we study their duals and characterize these spaces in terms of the growth of convolution averages of their elements. This characterization gives a canonical way to define a locally convex topology on these spaces and we give necessary and sufficient conditions for them to be ultrabornological. In particular, our results apply to spaces of convolutors for Gelfand--Shilov spaces.},
  author       = {Debrouwere, Andreas and Vindas Diaz, Jasson},
  issn         = {0025-584X},
  journal      = {MATHEMATISCHE NACHRICHTEN},
  language     = {eng},
  number       = {3},
  pages        = {573--602},
  title        = {On weighted inductive limits of spaces of ultradifferentiable functions and their duals},
  url          = {http://dx.doi.org/10.1002/mana.201700395},
  volume       = {292},
  year         = {2019},
}

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