## Linear Operators, Part 2 |

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Page 1148

Moreover, H is the direct sum of a finite number of groups H,-, each of which is

either (1) The additive group of the

complex unitary matrices of determinant 1; or (3) The group SpU(n) of all 2nX2n ...

Moreover, H is the direct sum of a finite number of groups H,-, each of which is

either (1) The additive group of the

**real axis**; or (2) The group SU(n) of all n><ncomplex unitary matrices of determinant 1; or (3) The group SpU(n) of all 2nX2n ...

Page 1214

For the kernels Wu we take those associated with the elements a in A as in

Lemma 9 so that the statements (a) and (b) are satisfied. From (b) it follows that )5

L[Wa(s,h)|2,u,,(dZ)1I(d8)< co, n g 1, for each bounded Borel set e of the

For the kernels Wu we take those associated with the elements a in A as in

Lemma 9 so that the statements (a) and (b) are satisfied. From (b) it follows that )5

L[Wa(s,h)|2,u,,(dZ)1I(d8)< co, n g 1, for each bounded Borel set e of the

**real axis**.Page 1550

E7 Suppose that for some (real or complex) 1 every solution of the equation (1—t

)f = 0 is of class L,(l ) and every ... Prove that the essential spectrum of the

operator T1(-r, p) is the positive semi-axis if n is even, and the entire

is odd.

E7 Suppose that for some (real or complex) 1 every solution of the equation (1—t

)f = 0 is of class L,(l ) and every ... Prove that the essential spectrum of the

operator T1(-r, p) is the positive semi-axis if n is even, and the entire

**real axis**if nis odd.

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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