## Linear Operators: Spectral theory |

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Page 1126

of the closed set C; we shall

. Since each projection in the spectral resolution of T and hence each continuous

function of T is a strong limit of linear combinations of the projections Eit it ...

of the closed set C; we shall

**denote**this subspace of L2[0, 1] by the symbol L2(C). Since each projection in the spectral resolution of T and hence each continuous

function of T is a strong limit of linear combinations of the projections Eit it ...

Page 1486

In the next few paragraphs t

operator of order n, defined on the interval R = {—co<t< +00}. Let t have the form

and suppose that all the coefficients ay are periodic and have the same period.

In the next few paragraphs t

**denotes**a formally self adjoint formal differentialoperator of order n, defined on the interval R = {—co<t< +00}. Let t have the form

and suppose that all the coefficients ay are periodic and have the same period.

Page 1636

In general, unless the contrary is explicitly stated, J, J, J, etc., will

for En, that is, indices whose range of variation is restricted by the condition min J

^ 1, max J n. The symbols Jv Jv J1 will similarly

In general, unless the contrary is explicitly stated, J, J, J, etc., will

**denote**indicesfor En, that is, indices whose range of variation is restricted by the condition min J

^ 1, max J n. The symbols Jv Jv J1 will similarly

**denote**indices for En+1. Thus ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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