## Linear Operators: Spectral theory |

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Page 1133

Then the kernels K, of Lemma 5 satisfy K,(s,t) = 0 unless either s : t or i = 1, j = 1,

and s and t lie in the same

kernels K., have this property, then 37 is a marimal family of subdiagonalizing ...

Then the kernels K, of Lemma 5 satisfy K,(s,t) = 0 unless either s : t or i = 1, j = 1,

and s and t lie in the same

**interval**of the complement of C. Conversely, if thekernels K., have this property, then 37 is a marimal family of subdiagonalizing ...

Page 1279

In this whole chapter, the letter I will denote an

be half-open; the

compact set ...

In this whole chapter, the letter I will denote an

**interval**of the real axis. The**interval**I can be open, half-open, or closed. The**interval**[a, oo) is considered tobe half-open; the

**interval**(–oo, + do) to be open. Thus a closed**interval**is acompact set ...

Page 1539

A4 Let t be a regular differential operator on the

complex number Å belongs to the essential spectrum of t if and only if there exists

a sequence {fi} of functions in o(To(t)) such that |f| = 1, f, vanishes in the

, ...

A4 Let t be a regular differential operator on the

**interval**[0, oo). Prove that acomplex number Å belongs to the essential spectrum of t if and only if there exists

a sequence {fi} of functions in o(To(t)) such that |f| = 1, f, vanishes in the

**interval**[0, ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero