## Linear Operators: Spectral theory |

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Page 1070

symbol Ke for a

same wav that there exists another

V2)(u)|1+edtt < Kejs |i?t(co)|1+eA*(Ať)- Since by Theorem 11 there exists a ...

symbol Ke for a

**constant**depending only on e and Qx). We may conclude in thesame wav that there exists another

**constant**K. such that (3) J|u|aa|v,(u)-(JST0i*V2)(u)|1+edtt < Kejs |i?t(co)|1+eA*(Ať)- Since by Theorem 11 there exists a ...

Page 1154

Since the product group J?<2) = RxR is locally compact and cr-compact, it has a

Haar measure A'*' defined on its Borel field Zm and what we shall prove is that for

some

Since the product group J?<2) = RxR is locally compact and cr-compact, it has a

Haar measure A'*' defined on its Borel field Zm and what we shall prove is that for

some

**constant**c, (fl<2>, 27<2), Xm) = c(R, Z, X) x (R, Z, X). Since it is clear that ...Page 1176

for n ^N, and /„(f ) for n > N. Then there exists a finite

such that the norm of 3fN, regarded as a mapping of LQ(lv) into itself, is at most C.

Proof of Lemma 24'. Subtracting a suitable

for n ^N, and /„(f ) for n > N. Then there exists a finite

**constant**C independent of Nsuch that the norm of 3fN, regarded as a mapping of LQ(lv) into itself, is at most C.

Proof of Lemma 24'. Subtracting a suitable

**constant**cn from each of the ...### 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