| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | March 10, 2003 |
| Latest Amendment Date: | April 7, 2005 |
| Award Number: | 0244515 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Joe W. Jenkins
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | May 1, 2003 |
| End Date: | April 30, 2007 (Estimated) |
| Total Intended Award Amount: | $285,245.00 |
| Total Awarded Amount to Date: | $285,245.00 |
| Funds Obligated to Date: |
FY 2004 = $95,003.00 FY 2005 = $99,265.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
121 UNIVERSITY HALL COLUMBIA MO US 65211-3020 (573)882-7560 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
121 UNIVERSITY HALL COLUMBIA MO US 65211-3020 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ANALYSIS PROGRAM |
| Primary Program Source: |
app-0104 app-0105 |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Abstract
Kalton
In this proposal, the aim is to study a number of problems
related to Banach space theory and its applications. Part
of the project deals with the theory of extensions of one
Banach space by another. For example it is planned to study
the problem of classifying those Banach spaces such that
every minimal extension is trivial. This problem can be
reformulated as a problem in approximation theory. It is
also planned to study applications to problems in the
nonlinear theory of Banach spaces, related to problems of
existence of uniform homeomorphisms between two Banach
spaces or between their unit balls. In a somewhat different
direction the proposer plans to continue his ongoing
research on Rademacher-bounded families of operators with
applications to sectorial operators and semigroups.
The theory of extensions can be considered in the following
terms. Suppose we are given a centrally symmetric solid in
three or more dimensions and we are allowed only to compute
its cross-section by a slice in some directions and the
shadow cast by the body in the perpendicular directions.
This gives us some information about the solid, but does not
permit complete reconstruction. The idea of studying
extensions is to obtain more complete information about the
body under certain additional conditions. Many questions of
importance in mathematical analysis and applications,
although not formally expressed in this way, can be
visualized in terms of extensions. Sectorial operators are
of importance in the basic theory of partial differential
equations of evolution type; such equations are very
important in physical applications. Typically a sectorial
operator is a differential operator acting on some suitable
space of functions. By understanding the properties of
sectorial operators and the semigroups they generate one
gains a better understanding of the behavior of solutions of
certain partial differential equations.
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