## Linear Operators: Spectral theory |

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Page 940

The unique measure whose existence is established in Theorem 1 is called the

Haar measure on the compact group G. By using Haar measure it will be shown

that the class of continuous functions on G which are

The unique measure whose existence is established in Theorem 1 is called the

Haar measure on the compact group G. By using Haar measure it will be shown

that the class of continuous functions on G which are

**finite dimensional**in the ...Page 1092

Let Q be a

of To; suppose that the dimension of 3 is d. Then, plainly, & is invariant under T

and T*, and, since (T&", w) = (3*, Toa.) = 0 for all a, we have T&H = 0 and similarly

...

Let Q be a

**finite**-**dimensional**space including both the range of T and the rangeof To; suppose that the dimension of 3 is d. Then, plainly, & is invariant under T

and T*, and, since (T&", w) = (3*, Toa.) = 0 for all a, we have T&H = 0 and similarly

...

Page 1146

M. Any

irreducible representations. This theorem shows that in studying

generality, ...

M. Any

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

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

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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