Hilbert space methods in signal processing
Rodney A. Kennedy, Parastoo Sadeghi.
Bok Engelsk 2013 · Electronic books.
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| Utgitt | Cambridge, England : : Cambridge University Press, , c2013.
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| Omfang | 1 online resource (440 p.)
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| Opplysninger | Description based upon print version of record.. - Contents; Preface; Part I Hilbert Spaces; 1 Introduction; 1.1 Introduction to Hilbert spaces; 1.1.1 The basic idea; 1.1.2 Application domains; 1.1.3 Broadbrush structure; 1.1.4 Historical comments; 1.2 Infinite dimensions; 1.2.1 Why understand and study infinity?; 1.2.2 Primer in transfinite cardinals; 1.2.3 Uncountably infinite sets; 1.2.4 Continuumas a power set; 1.2.5 Countable sets and integration; 2 Spaces; 2.1 Space hierarchy: algebraic,metric, geometric; 2.2 Complex vector space; 2.3 Normed spaces and Banach spaces; 2.3.1 Norm and normed space. - 2.3.2 Convergence concepts in normed spaces2.3.3 Denseness and separability; 2.3.4 Completeness of the real numbers; 2.3.5 Completeness in normed spaces; 2.3.6 Completion of spaces; 2.3.7 Complete normed spaces-Banach spaces; 2.4 Inner product spaces and Hilbert spaces; 2.4.1 Inner product; 2.4.2 Inner product spaces; 2.4.3 When is a normed space an inner product space?; 2.4.4 Orthonormal sets and sequences; 2.4.5 The space l2; 2.4.6 The space L2(Ω); 2.4.7 Inner product and orthogonality with weighting in L2(Ω); 2.4.8 Complete inner product spaces-Hilbert spaces. - 2.5 Orthonormal polynomials and functions2.5.1 Legendre polynomials; 2.5.2 Hermite polynomials; 2.5.3 Complex exponential functions; 2.5.4 Associated Legendre functions; 2.6 Subspaces; 2.6.1 Preamble; 2.6.2 Subsets,manifolds and subspaces; 2.6.3 Vector sums, orthogonal subspaces and projections; 2.6.4 Projection; 2.6.5 Completeness of subspace sequences; 2.7 Complete orthonormal sequences; 2.7.1 Definitions; 2.7.2 Fourier coefficients and Bessel's inequality; 2.8 On convergence; 2.8.1 Strong convergence; 2.8.2 Weak convergence; 2.8.3 Pointwise convergence; 2.8.4 Uniform convergence. - 2.9 Examples of complete orthonormal sequences2.9.1 Legendre polynomials; 2.9.2 Bessel functions; 2.9.3 Complex exponential functions; 2.9.4 Spherical harmonic functions; 2.10 Gram-Schmidt orthogonalization; 2.10.1 Legendre polynomial construction; 2.10.2 Orthogonalization procedure; 2.11 Completeness relation; 2.11.1 Completeness relation with weighting; 2.12 Taxonomy of Hilbert spaces; 2.12.1 Non-separable Hilbert spaces; 2.12.2 Separable Hilbert spaces; 2.12.3 The big (enough) picture; Part II Operators; 3 Introduction to operators; 3.1 Preamble; 3.1.1 A note on notation. - 3.2 Basic presentation and properties of operators3.3 Classification of linear operators; 4 Bounded operators; 4.1 Definitions; 4.2 Invertibility; 4.3 Boundedness and continuity; 4.4 Convergence of a sequence of bounded operators; 4.5 Bounded operators as matrices; 4.6 Completing the picture: bounded operator identities; 4.7 Archetype case: Hilbert-Schmidt integral operator; 4.7.1 Some history and context; 4.7.2 Hilbert-Schmidt integral operator definition; 4.7.3 Matrix presentation and relations; 4.8 Road map; 4.9 Adjoint operators; 4.9.1 Special forms of adjoint operators. - 4.10 Projection operators. - An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.
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| Emner | |
| Sjanger | |
| Dewey | 621.38220151 . - 515.733
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| ISBN | 9781107010031
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