## Linear Operators, Part 2 |

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Page 1064

Q(u) <1) go) —l , /<w-um mgi lul

Q(w)|,u(dw). To do this, let {QM} be a sequence of odd functions, each infinitely

often differentiable in the neighborhood of the unit sphere, such that .Q,,,(t:c) = .

Q(u) <1) go) —l , /<w-um mgi lul

**satisfies**the inequality |g|,, g 1A,]/lp, where I = Is|.Q(w)|,u(dw). To do this, let {QM} be a sequence of odd functions, each infinitely

often differentiable in the neighborhood of the unit sphere, such that .Q,,,(t:c) = .

Page 1164

Calderon and Zygmund [1] show that if the function Q

weak, continuity hypothesis, then the singular integral Q __ no =] ('T ”,)/(my E" |~'?

—!/| (i) exists for almost all x iff is in L1(E")or L,(E"), 00> p > 1, (cf. Exercise 8.23); ...

Calderon and Zygmund [1] show that if the function Q

**satisfies**a suitable, ratherweak, continuity hypothesis, then the singular integral Q __ no =] ('T ”,)/(my E" |~'?

—!/| (i) exists for almost all x iff is in L1(E")or L,(E"), 00> p > 1, (cf. Exercise 8.23); ...

Page 1602

r)f = 0 on [0, oo) which is not square-integrable but which

Ow) for some k > 0. Then the point 2. belongs to the essential spectrum of 1' (

Wintner [17]). (49) Suppose that the function q is bounded below, and that for

some ...

r)f = 0 on [0, oo) which is not square-integrable but which

**satisfies**[J1/<s>|=d-I =Ow) for some k > 0. Then the point 2. belongs to the essential spectrum of 1' (

Wintner [17]). (49) Suppose that the function q is bounded below, and that for

some ...

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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