Titlebook: Basic Classes of Linear Operators; Israel Gohberg,Seymour Goldberg,Marinus A. Kaashoe Textbook 2003 Springer Basel AG 2003 Hilbert space.O

法律的瑕疵

https://doi.org/10.1007/978-3-476-00202-0A norm can be defined on ?. in many different ways. Some of them stem from an inner product. An example of a norm on ?. which does not arise from an inner product is ∥(α.,α., …, α.)∥ = max

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寄生蟲

https://doi.org/10.1007/978-3-476-00360-7A linear operator . defined in the standard basis of ?.(1 ≤ . ≤ ∞) by a matrix of the form ., with . ∈ ? and . we call a Poincaré operator.

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Hilbert Spaces,In this chapter we review the main properties of the complex .-dimensional space ?. and then we study the Hilbert space which is its most natural infinite dimensional generalization. Many applications to classical problems are included (Least squares, Fourier series and others).

幼稚

Spectral Theory of Compact Self Adjoint Operators,One of the fundamental results in linear algebra is the spectral theorem which states that if . is a finite dimensional Hilbert space and . ∈ .(.) is self adjoint, then there exists an orthonormal basis ?.,…, ?. for . and real numbers λ.,…, λ. such that

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Oscillations of an Elastic String,The aim of this chapter is to describe the motion of a vibrating string in terms of the eigenvalues and eigenvectors of an integral operator.

尖叫

Operational Calculus with Applications,The spectral theory which was studied in the preceding chapters provides a means for the development of a theory of functions of a compact self adjoint operator. We now present this theory with applications to a variety of problems in differential equations.

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Solving Linear Equations by Iterative Methods,In this chapter we return to the problem of solving the equation . — . = .. One of the themes of this book is to devise algorithms which generate a sequence of vectors that converges to a solution. This chapter further develops this theme. The main results rely on the spectral theorem.

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