## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 84

Page 1074

is the Fourier

in Exercise 6. 10 Let à be a function defined on (– 60, -i- oc) which is of finite total

...

is the Fourier

**transform**of a function in Lp(–oo, + oy whenever F is the Fourier**transform**of a function in Lp(– o, + Co.), the Fourier**transforms**being defined asin Exercise 6. 10 Let à be a function defined on (– 60, -i- oc) which is of finite total

...

Page 1075

27 J–4 F denoting the Fourier

c) dr & Co. A > 0 16 Show that not every continuous function, defined for - 30 < t <

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

27 J–4 F denoting the Fourier

**transform**of f, fails to satisfy the inequality sup s f4(c) dr & Co. A > 0 16 Show that not every continuous function, defined for - 30 < t <

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

**transform**...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 Q(T) dense ...

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 Q(T) dense ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero