Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
Seiten
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space ( Omega,§igma,μ)) and with values in a Banach space X can be extended to a sort of optimal domain.
Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L¹(m₊T), the space of all functions integrable with respect to the vector measure m₊T associated with T, and the optimal extension of T turns out to be the integration operator I₊m₊T.
In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fréchet function spaces X(μ) (this time over a σ-finite measure space ( Omega,§igma,μ)).
It is shown that under similar assumptions on X(μ) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation.
In a further step the newly gained results are applied to four well-known operators defined on the Fréchet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p₊ textloc( mathbbR).
Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L¹(m₊T), the space of all functions integrable with respect to the vector measure m₊T associated with T, and the optimal extension of T turns out to be the integration operator I₊m₊T.
In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fréchet function spaces X(μ) (this time over a σ-finite measure space ( Omega,§igma,μ)).
It is shown that under similar assumptions on X(μ) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation.
In a further step the newly gained results are applied to four well-known operators defined on the Fréchet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p₊ textloc( mathbbR).
Die Kunst der Übersetzung
| Erscheinungsdatum | 02.10.2017 |
|---|---|
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Einbandart | Paperback |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Fréchet function spaces • Optimal domain process • vector measures |
| ISBN-10 | 3-8325-4557-3 / 3832545573 |
| ISBN-13 | 978-3-8325-4557-4 / 9783832545574 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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