## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 87

Page 942

Now if Ts<p = X<p then jGS(su~1Mu)fi(du) = Xq>(s), seG, is a

. By replacing s by st and u by ut and using the fact that fi(Et) = fJ.(E) it is seen that

i.e., every translate <p* of an eigenfunction <p corresponding to X is also an ...

Now if Ts<p = X<p then jGS(su~1Mu)fi(du) = Xq>(s), seG, is a

**continuous function**. By replacing s by st and u by ut and using the fact that fi(Et) = fJ.(E) it is seen that

i.e., every translate <p* of an eigenfunction <p corresponding to X is also an ...

Page 966

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

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

agrees almost everywhere with a

of ...

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

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

agrees almost everywhere with a

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

Page 1002

5 A

if for each e > 0 there exists a number ... Show that every such almost periodic

function may be approximated uniformly by linear combinations of functions of

the ...

5 A

**continuous function**/ of two real variables x = (xv x2) is called almost periodicif for each e > 0 there exists a number ... Show that every such almost periodic

function may be approximated uniformly by linear combinations of functions of

the ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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