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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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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, ULTRADISTRIBUTIONS, HYPERFUNCTIONS, COMPLETENESS, CONVOLUTION, TRANSFORM, THEOREMS

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MLA
Debrouwere, Andreas, and Jasson Vindas Diaz. “On Weighted Inductive Limits of Spaces of Ultradifferentiable Functions and Their Duals.” MATHEMATISCHE NACHRICHTEN, vol. 292, no. 3, 2019, pp. 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.
Chicago author-date
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.
Chicago author-date (all authors)
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.
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.
IEEE
[1]
A. Debrouwere and J. Vindas Diaz, “On weighted inductive limits of spaces of ultradifferentiable functions and their duals,” MATHEMATISCHE NACHRICHTEN, vol. 292, no. 3, pp. 573–602, 2019.
@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},
  keywords     = {completeness of inductive limits,convolution Gelfand-Shilov spaces,short‐time Fourier transform,ultrabornological (PLS)‐spaces,ULTRADISTRIBUTIONS,HYPERFUNCTIONS,COMPLETENESS,CONVOLUTION,TRANSFORM,THEOREMS},
  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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