: 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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Interpolation spaces: an introduction – Jöran Bergh, Jörgen Löfström – Google Books
Functional Analysis Retrieved from ” https: Further information on the Library’s opening hours is available at: The family of L p spaces consisting of complex valued functions interpolwtion well under complex interpolation. Banach spaces Sobolev spaces Fourier analysis. Lions and Peetre have proved that:. Interpolation does not depend only upon the isomorphic nor isometric equivalence classes of X 0 and X 1. A complex interpolation space is usually not isomorphic interpolatlon one of the spaces given by the real interpolation method.
CS1 French-language sources fr. In the field of mathematical analysis lofstro, an interpolation space is a space which lies “in between” two other Banach spaces. For the rest of the section, the following setting and notation will be used:.
The optimal choice of s leads to the formula . You can view this on the NLA website. If the scalars are complex numbersproperties of complex analytic functions are used to define an interpolation space.
Order a copy Copyright or permission restrictions may apply. In the Library Request this item to view in the Library’s reading rooms using your library card. It depends in an essential way from the specific relative position that X 0 and X 1 occupy in a larger space Z. How do I find a book?
Other such questions are compactness or weak-compactness of linear operators. 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.
This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple. Interpolation studies the family of spaces X that are intermediate spaces between X 0 and X 1 in the sense that.
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BookOnline – Google Books. However, there is a general relationship.
This fact is closely related to the Riesz—Thorin theorem. That the J- and K-methods agree is important for the study of duals of interpolation spaces: Can I borrow this item? New search User lists Site feedback Ask a librarian Help. The theorem covers degenerate cases that have not been excluded: Advanced search Search history. National Library of Australia. Equipped with these norms, the intersection and the sum are Banach spaces.
Collection delivery service resumes on Wednesday 2 January In the special case where X 0 is continuously embedded in X 1one can omit the part of the series with negative indices n. This abstract method can be used, for example, for the proof of the following result:.