## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 55

Page 1290

is

way, the formal differential operator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is

observations ...

is

**formally self adjoint**provided only that the coefficients p, are real. In the sameway, the formal differential operator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is

**formally self adjoint**provided that p(t) is a real function. If we use theseobservations ...

Page 1295

If the (regular or irregular) formal differential operator r is

the operator To(t) is symmetric. PRoof. Clearly To(r) C T1(t). Corollary 5 shows

that Ti(r) C To(r)*. Q.E.D. We recall (cf. Definition XII.4.9) that if r is formally self ...

If the (regular or irregular) formal differential operator r is

**formally self adjoint**thenthe operator To(t) is symmetric. PRoof. Clearly To(r) C T1(t). Corollary 5 shows

that Ti(r) C To(r)*. Q.E.D. We recall (cf. Definition XII.4.9) that if r is formally self ...

Page 1400

Let t be a

with at least one fired endpoint. ... Then the deficiency indices of t are both equal

to an integer k and (a) for every self adjoint eatension T of To(t), the dimension of

...

Let t be a

**formally self adjoint**formal differential operator defined on an interval Iwith at least one fired endpoint. ... Then the deficiency indices of t are both equal

to an integer k and (a) for every self adjoint eatension T of To(t), the dimension of

...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 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