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- W4313352641 abstract "The goal of this chapter is to give an elementary but comprehensive introduction to the theory of Hilbert spaces, where we wish to highlight the many-faceted interplay of their geometric and analytic properties. This culminates in the theorem of Riesz–Fréchet, which describes continuous linear forms in a Hilbert space. Important for us will be that this theorem can be interpreted as an existence and uniqueness result. A generalization known as the Lax–Milgram theorem, which we will give in Section 4.5, is at the heart of the solution theory of elliptic equations which we will present in Chapters 5 , 6 and 7 . For the reader who is principally interested in these equations, the part of the current chapter up to and including Section 4.5 provides sufficient background." @default.
- W4313352641 created "2023-01-06" @default.
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- W4313352641 date "2022-08-26" @default.
- W4313352641 modified "2023-10-16" @default.
- W4313352641 title "Hilbert spaces" @default.
- W4313352641 cites W4253741862 @default.
- W4313352641 doi "https://doi.org/10.1007/978-3-031-13379-4_4" @default.
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