Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Functional Analysis

arXiv:1405.0111 (math)
[Submitted on 1 May 2014 (v1), last revised 24 Aug 2015 (this version, v2)]

Title:The wavelet transforms in Gelfand-Shilov spaces

Authors:Stevan Pilipovic, Dusan Rakic, Nenad Teofanov, Jasson Vindas
View PDF
Abstract:We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calderón reproducing formula) in the context of ultradistributions.
Subjects: Functional Analysis (math.FA)
MSC classes: 42C40, 46F05, 46F12
Cite as: arXiv:1405.0111 [math.FA]
  (or arXiv:1405.0111v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1405.0111
Journal reference: Collect. Math. 67 (3) (2016), 443-460
Related DOI: https://doi.org/10.1007/s13348-015-0154-y

Submission history

From: Nenad Teofanov M [view email]
[v1] Thu, 1 May 2014 08:02:24 UTC (21 KB)
[v2] Mon, 24 Aug 2015 07:41:54 UTC (20 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.FA
< prev   |   next >
new | recent | 2014-05
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)