Conservativeness and Extensions of Feller Semigroups

Conservativeness and Extensions of Feller Semigroups Let $$\{ T_t \} _{t \geqslant 0} $$ denote a Feller semigroup on $$C_\infty (\mathbb{R}^n )$$ , and $$\{ \tilde T_t \} _{t \geqslant 0} $$ itsextension to the bounded measurable functions. We show that $$T_t 1 \in C_b (\mathbb{R}^n )$$ . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Conservativeness and Extensions of Feller Semigroups

Loading next page...
 
/lp/springer_journal/conservativeness-and-extensions-of-feller-semigroups-d0SzH6kz3a
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009748105208
Publisher site
See Article on Publisher Site

Abstract

Let $$\{ T_t \} _{t \geqslant 0} $$ denote a Feller semigroup on $$C_\infty (\mathbb{R}^n )$$ , and $$\{ \tilde T_t \} _{t \geqslant 0} $$ itsextension to the bounded measurable functions. We show that $$T_t 1 \in C_b (\mathbb{R}^n )$$ . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.

Journal

PositivitySpringer Journals

Published: Oct 7, 2004

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 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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