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210512 ||| eng |
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|a 4557
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|a 9783832545574
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|a Blaimer, Bettina
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|a Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
|h Elektronische Ressource
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| 260 |
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|a Berlin/Germany
|b Logos Verlag Berlin
|c 2017
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| 300 |
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|a 1 electronic resource (137 p.)
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| 653 |
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|a Optimal domain process
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| 653 |
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|a Fréchet function spaces
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| 653 |
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|a Calculus and mathematical analysis / bicssc
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| 653 |
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|a Vector measures
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b DOAB
|a Directory of Open Access Books
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| 500 |
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|a Creative Commons (cc), https://creativecommons.org/licenses/by-nc-nd/4.0/
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|a 10.30819/4557
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|u https://www.logos-verlag.de/ebooks/OA/978-3-8325-4557-4.pdf
|7 0
|x Verlag
|3 Volltext
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|u https://directory.doabooks.org/handle/20.500.12854/64485
|z DOAB: description of the publication
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|a 500
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|a 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 L±(mâ T), the space of all functions integrable with respect to the vector measure mâ T associated with T, and the optimal extension of T turns out to be the integration operator Iâ mâ 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 Ï -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 pâ textloc( mathbbR).
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