## Linear Operators, Part 2 |

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Page 1130

Conversely, if K“ is any family of

Hilbert-Schmidt operator in {)0 with norm given by (iv). Pnoor. Let A = [0, 1] ><N,

where N is the set of all integers n g 1. If we regard N as a measure space, each ...

Conversely, if K“ is any family of

**kerneLs*** satisfying (i), . . ., (iv), then (v) defines aHilbert-Schmidt operator in {)0 with norm given by (iv). Pnoor. Let A = [0, 1] ><N,

where N is the set of all integers n g 1. If we regard N as a measure space, each ...

Page 1590

For a detailed exposition of the problems connected with the calculation of the

Green's

Mohr [1] may be found valuable. Section 4. The work of Hilbert [1] in 1904 already

...

For a detailed exposition of the problems connected with the calculation of the

Green's

**kernel**for a differential operator on a finite interval, the recent paper of E.Mohr [1] may be found valuable. Section 4. The work of Hilbert [1] in 1904 already

...

Page 1624

as a “linear combination” of the functions cos t\/I in terms of an integral operator

with a

indicate briefly how the

as a “linear combination” of the functions cos t\/I in terms of an integral operator

with a

**kernel**of Volterra type: (>2) f(t,l) = cos t\/1+)-otK1(t,s)cos s\/Ids. Let usindicate briefly how the

**kernel**K1 is obtained once the functions f(t, 1) are known.### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma 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