| 書目名稱 | Elements of Hilbert Spaces and Operator Theory | | 編輯 | Harkrishan Lal Vasudeva | | 視頻video | http://file.papertrans.cn/308/307593/307593.mp4 | | 概述 | Presents an introduction to the geometry of Hilbert spaces and operator theory.Discusses Legendre, Hermite, Laguerre polynomials and Rademacher functions and their applications.Highlights applications | | 圖書封面 |  | | 描述 | .The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also d | | 出版日期 | Book 2017 | | 關鍵詞 | Linear operators; Special theory; Banach Spaces; Riesz Lemma; Finite Dimensional Spaces; Operator theory; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-10-3020-8 | | isbn_softcover | 978-981-10-9765-2 | | isbn_ebook | 978-981-10-3020-8 | | copyright | Springer Nature Singapore Pte Ltd. 2017 |
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