: Interpolation Spaces (Grundlehren der mathematischen Wissenschaften) (): J. Bergh, J. Lofstrom: Books. Citation. Bennett, Colin. Review: Jöran Bergh and Jörgen Löfström, Interpolation spaces, an introduction. Bull. Amer. Math. Soc. 84 (), no. 1, Interpolation spaces: an introduction. Front Cover. Jöran Bergh, Jörgen Löfström. Springer, – Mathematics – pages.

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The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual.

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We will brgh you if interpolatiin. Order a copy Copyright or permission restrictions may apply. That the J- and K-methods agree is important for the study of duals of interpolation spaces: The main applications are in Sobolev spaceswhere spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives. In the development of Sobolev spaces, it became clear that the trace spaces were not any of the usual function spaces with integer number of derivativesand Jacques-Louis Lions discovered that indeed these trace spaces were constituted of functions that have a noninteger degree of differentiability.

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This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple. Other such questions are compactness or weak-compactness of linear operators. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen ; If the scalars are complex numbersproperties of complex analytic functions are used to define an interpolation space.

See what’s been added to the collection in the current 1 2 3 4 5 6 weeks months years. BookOnline – Google Books. Let X 0X 1 be a compatible couple of Banach spaces. Further information on the Library’s opening hours is available at: Can I get a copy?

Several interpolation results are available for Sobolev spaces and Besov spaces on R n[26].

Interpolation does not depend only upon the isomorphic nor isometric equivalence classes of X 0 and X 1. Members of Aboriginal, Torres Strait Islander and Maori communities are advised that this catalogue contains names and images of deceased people. The optimal choice of s leads to the formula [9]. For the rest of the section, the following setting and notation will be used:. However, there is a general relationship. The first and most commonly used when actually identifying examples of interpolation spaces is the K-method.

Lions and Peetre have proved that:. Real interpolation between Spsces p spaces gives [13] the family of Lorentz spaces. A complex interpolation space is usually not isomorphic to one of the spaces given by the real interpolation method.

How do I find a book? From 25 December to 1 Januarythe Library’s Reading Rooms will be closed and no collection requests will intdrpolation filled. A compatible couple X 0X 1 of Banach spaces consists of two Banach spaces X 0 and X 1 that are continuously embedded in the same Hausdorff topological vector space Spacees.

This is because the K-functional K ft ; X 0X 1 of this couple is equivalent to. It depends in an essential way from the specific relative position that X 0 and X 1 occupy in a larger space Z.

## Interpolation space

Details Collect From You must be logged in to Tag Records. The theorem covers degenerate cases that have not been excluded: To learn more about how to request items watch this short online video. In simple terms, if a linear function is continuous on a certain space L p and also on a certain space L qthen it is also continuous on the space L rfor any intermediate lofstorm between p and q.

Retrieved from ” https: You can view this on the NLA website. This fact is closely related to the Riesz—Thorin theorem. Can I borrow this item?

### Interpolation Spaces: An Introduction – Jöran Bergh, Jörgen Löfström – Google Books

Paris in French Interpolation studies the family of spaces X that are intermediate spaces between X 0 interpoaltion X 1 in the sense that. The following inclusions are all continuous:.

From Wikipedia, the free encyclopedia. Equipped with these norms, the intersection and the sum are Banach spaces. Banach spaces Sobolev spaces Fourier analysis.

The family of L p spaces consisting of complex valued functions behaves well under complex interpolation. This page was last edited on 28 Marchat