## Linear Operators, Part 2 |

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Page 942

8 E G. is a

that ;4(Et) =,u(E) it is seen that f,,g<w-1>¢<u¢>t<du> = tow). i.e., every translate

zp' of an eigenfunction (p corresponding to 1 is also an eigenfunction ...

8 E G. is a

**continuous function**. By replacing s by st and u by ut and using the factthat ;4(Et) =,u(E) it is seen that f,,g<w-1>¢<u¢>t<du> = tow). i.e., every translate

zp' of an eigenfunction (p corresponding to 1 is also an eigenfunction ...

Page 966

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma l(d), the integral on the left of [-1-] is continuous, we conclude that hm

agrees almost everywhere with a

of ...

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma l(d), the integral on the left of [-1-] is continuous, we conclude that hm

agrees almost everywhere with a

**continuous function**. By redefining hm on a setof ...

Page 1002

4 If f is a non-negative function in AP, and M (/) = 0 (in the notation of Exercise 2)

then f = 0. 5 A

almost periodic if for each a > 0 there exists a number L(s) such that each circle in

...

4 If f is a non-negative function in AP, and M (/) = 0 (in the notation of Exercise 2)

then f = 0. 5 A

**continuous function**f of two real variables .1: = (a:1,.1:2) is calledalmost periodic if for each a > 0 there exists a number L(s) such that each circle in

...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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