## Linear Operators, Part 2 |

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Page 940

The function f is said to be

the proof of the following theorem and so the field of scalars is taken to be the

field ...

The function f is said to be

**finite dimensional**if its set {f' |seG} of translates is a**finite dimensional**vector space of functions. The spectral theorem will be used inthe proof of the following theorem and so the field of scalars is taken to be the

field ...

Page 1092

(I I there are only a finite number N of non-zero eigenvalues, we write 1,,(T) = 0, n

> N). Then, for each ... time in what follows. Let 6 be a

including both the range of T and the range of T*; suppose that the dimension of ...

(I I there are only a finite number N of non-zero eigenvalues, we write 1,,(T) = 0, n

> N). Then, for each ... time in what follows. Let 6 be a

**finite**-**dimensional**spaceincluding both the range of T and the range of T*; suppose that the dimension of ...

Page 1146

Any

irreducible representations. This theorem shows that in studying

generality, confine ...

Any

**finite dimensional**representation of a compact group G is a direct sum 0/irreducible representations. This theorem shows that in studying

**finite****dimensional**representations of a compact group G we may, without loss ofgenerality, confine ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

13 other sections not shown

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero