Semi-classical Time-frequency Analysis and Applications

Semi-classical Time-frequency Analysis and Applications This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schrödinger type equations. Indeed, continuity results of both Schrödinger propagators and their asymptotic solutions are obtained on ℏ $\hbar $ -dependent Banach spaces, the semi-classical version of the well-known modulation spaces. Moreover, their operator norm is controlled by a constant independent of the Planck’s constant ℏ $\hbar $ . The main tool in our investigation is the joint application of standard approximation techniques from semi-classical analysis and a generalized version of Gabor frames, dependent of the parameter ℏ $\hbar $ . Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Mathematical Physics, Analysis and Geometry" Springer Journals

Semi-classical Time-frequency Analysis and Applications

Loading next page...
 
/lp/springer_journal/semi-classical-time-frequency-analysis-and-applications-BgHn7PLY0T
Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Analysis; Geometry; Group Theory and Generalizations; Applications of Mathematics
ISSN
1385-0172
eISSN
1572-9656
D.O.I.
10.1007/s11040-017-9259-8
Publisher site
See Article on Publisher Site

Abstract

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schrödinger type equations. Indeed, continuity results of both Schrödinger propagators and their asymptotic solutions are obtained on ℏ $\hbar $ -dependent Banach spaces, the semi-classical version of the well-known modulation spaces. Moreover, their operator norm is controlled by a constant independent of the Planck’s constant ℏ $\hbar $ . The main tool in our investigation is the joint application of standard approximation techniques from semi-classical analysis and a generalized version of Gabor frames, dependent of the parameter ℏ $\hbar $ . Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated.

Journal

"Mathematical Physics, Analysis and Geometry"Springer Journals

Published: Nov 30, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off