## Linear Operators: Spectral theory |

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Page 1175

Then x^i is a bounded

real So, let /, be the

5 - 5, 0 otherwise. By Corollary 22, it follows that there is a finite constant C" such

...

Then x^i is a bounded

**mapping**of the space L,(L,(S)) into itself. Proof. For eachreal So, let /, be the

**mapping**in L,(L,(S)) defined by the formula (47) (*,f)(3) = f(5),5 - 5, 0 otherwise. By Corollary 22, it follows that there is a finite constant C" such

...

Page 1669

Let M : II – I, be a

whenever C is a compact subset of I2; (b) (M(.)), e C*(I), j = 1,..., n2. Then (i) for

each p in C*(I2), p o M will denote the function p in C*(II) defined, for a in II, by the

...

Let M : II – I, be a

**mapping**of I1 into I, such that (a) M-'C is a compact subset of I1whenever C is a compact subset of I2; (b) (M(.)), e C*(I), j = 1,..., n2. Then (i) for

each p in C*(I2), p o M will denote the function p in C*(II) defined, for a in II, by the

...

Page 1707

Hence, by Lemma 3.41, to-i-A is a continuous

of Hot”(C) onto Ho (C), for all k between – o and + o. Let ve and so be the norms

of the

Hence, by Lemma 3.41, to-i-A is a continuous

**mapping**with a continuous inverseof Hot”(C) onto Ho (C), for all k between – o and + o. Let ve and so be the norms

of the

**map**to-1-2 : Hot" (C) → Ho (C) and of its inverse, respectively. Let vi = to ...### What people are saying - Write a review

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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