Abstract
Throughout this book, we use the theory of generalized functions, and it is convenient to present this theory within the framework of the abstract scheme of rigged spaces. In this case, Hilbert riggings are initial, and the role of the classical Sobolev-Schwartz chain D⊥(ℝd) ⊃ L 2(ℝd) ⊃ D(ℝd) is played by the chain of Hilbert spaces H − ⊃ H 0 ⊃ H + which consists of the space H + of “test” (positive) vectors, the space H − (dual to H +) of “generalized” (negative) vectors, and the “zero” space H 0 setting the duality. These constructions are now well known and frequently used. Nevertheless, in Section 1, we give the necessary information with proofs (sometimes concise).
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© 1995 Springer Science+Business Media Dordrecht
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Berezansky, Y.M., Kondratiev, Y.G. (1995). Rigged Spaces. In: Spectral Methods in Infinite-Dimensional Analysis. Mathematical Physics and Applied Mathematics, vol 12/1-2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0509-5_1
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DOI: https://doi.org/10.1007/978-94-011-0509-5_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4227-7
Online ISBN: 978-94-011-0509-5
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