## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 93

Page 1074

Show that if 1 < p < 2, and if F is the Fourier

), then so is A(*)P('). Fourier

Use the inequality of M. Riesz.) 11 Let A, be a sequence defined for – od 3 n ...

Show that if 1 < p < 2, and if F is the Fourier

**transform**of a function in L,(—oo, +oo), then so is A(*)P('). Fourier

**transforms**are to be defined as in Exercise 6. (Hint:Use the inequality of M. Riesz.) 11 Let A, be a sequence defined for – od 3 n ...

Page 1075

27 J–4 F denoting the Fourier

(r)|da. ~. o. A-0 16 Show that not every continuous function, defined for —oo - t <

00 and approaching zero as t approaches + o or – o, is the Fourier

27 J–4 F denoting the Fourier

**transform**of f, fails to satisfy the inequality sup. s. fA(r)|da. ~. o. A-0 16 Show that not every continuous function, defined for —oo - t <

00 and approaching zero as t approaches + o or – o, is the Fourier

**transform**of ...Page 1271

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley

self adjoint extension. Let T be a symmetric operator with domain o[T) dense in ...

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley

**transform**can be used to determine when a symmetric operator has aself adjoint extension. Let T be a symmetric operator with domain o[T) dense in ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

38 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero