## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 65

Page 1074

8 Show , with the hypotheses and notation of Exercise 6 , that if b is in Lol - 00 , +

00 ) , then sto 16 ( t ) | 2 - - | F ( t ) | pdt < 0 . 9 Let 2 be a real function of a real

variable such that 2 ( • ) F ( : ) is the

00 ) ...

8 Show , with the hypotheses and notation of Exercise 6 , that if b is in Lol - 00 , +

00 ) , then sto 16 ( t ) | 2 - - | F ( t ) | pdt < 0 . 9 Let 2 be a real function of a real

variable such that 2 ( • ) F ( : ) is the

**Fourier**transform of a function in Lj ( - 00 , +00 ) ...

Page 1075

15 Show that there exists a function f in L ( - 00 , + 00 ) for which the family of

functions 1 p + A f ( x ) = - T F ( t ) e - itx dt , 21 J - A F denoting the

transform of f , fails to satisfy the inequality sup A > OJ ( x ) \ dx < 0 . 16 Show that

not every ...

15 Show that there exists a function f in L ( - 00 , + 00 ) for which the family of

functions 1 p + A f ( x ) = - T F ( t ) e - itx dt , 21 J - A F denoting the

**Fourier**transform of f , fails to satisfy the inequality sup A > OJ ( x ) \ dx < 0 . 16 Show that

not every ...

Page 1178

Let M be the mapping in L ( 12 ) which maps the vector - valued function whose

nth component has the

whose nth component has the

...

Let M be the mapping in L ( 12 ) which maps the vector - valued function whose

nth component has the

**Fourier**transform ģ ( 5 ) into the vector - valued functionwhose nth component has the

**Fourier**transform hn ( 5 ) defined by ( 61 ) hu ( 5 )...

### What people are saying - Write a review

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

### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 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

additive adjoint operator 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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero