: 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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See what’s been added to the collection in the current 1 2 3 4 5 6 weeks months years. Banach spaces Sobolev spaces Fourier analysis.
Interpolation Spaces: An Introduction – Jöran Bergh, Jörgen Löfström – Google Books
The K-method of real interpolation  can be used for Banach intrpolation over the field R of real numbers. Can I get a copy?
Views Slaces Edit View history. The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual. Retrieved from ” https: In the field of mathematical analysisan interpolation space is a space which lies “in between” two other Banach spaces. You can view this on the NLA website. Other such questions are compactness or weak-compactness of linear operators.
To learn more about Copies Direct watch this short online video. A Banach space X is said to be continuously embedded in a Hausdorff topological vector space Z when X is a linear subspace of Z such that the inclusion map from X into Z is continuous.
This page was last edited on 28 Marchat This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple. In other words, L r is a space which is intermediate between L p and L q. Order a copy Copyright or permission restrictions may apply. Functional Analysis The theorem covers degenerate cases that have not been excluded: Collection delivery service resumes on Wednesday 2 January Catalogue Persistent Identifier https: New search User lists Site feedback Ask a librarian Help.
Details Collect From In the special case where X 0 is continuously embedded in X 1one can omit the part of the series with negative indices n.
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Interpolation does not depend only upon the isomorphic nor isometric equivalence classes of X 0 and X 1. Changing the order of the two spaces results in: There are two ways for introducing the real interpolation method. Real interpolation between L p spaces gives  the family of Lorentz spaces.
CS1 French-language sources fr. This is because the K-functional K ft ; X 0X 1 of this couple is equivalent to.
Interpolation spaces: an introduction – Jöran Bergh, Jörgen Löfström – Google Books
However, there is a general relationship. National Library lofxtrom Australia. Browse titles authors subjects uniform titles series callnumbers dewey numbers starting from optional. Request this item to view in the Library’s reading rooms using your library card. Let X 0X 1 be a compatible couple of Banach spaces.
If the scalars are complex numbersproperties of complex analytic functions are used to define an interpolation space. Many methods were designed to generate such spaces of functions, including the Fourier transformcomplex interpolation,  real interpolation,  as well as other tools see e. That the J- and K-methods agree is important for the study of duals of interpolation spaces: For the rest of the section, the following setting and notation will be used:.
Can I view this online? Cite this Email this Add to favourites Print this page. Can I spaaces this item? 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 interoolation continuous on the space L rfor any intermediate r between p and q. Further information on the Library’s opening hours is available at: We will contact you if necessary.
The first and most commonly used when actually identifying examples of interpolation spaces is the K-method. The family of L p spaces consisting of complex valued functions behaves well under complex interpolation.