## Linear Operators, Part 2 |

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Results 1-3 of 60

Page 1074

(Hint: Cf. IV.4.19.) 8 Show, with the hypotheses and notation of Exercise 6, that if

b is in L,(—oo, +00), then |b(t)[=-"|F(t)]"dt < oo. 9 Let A be a real function of a real

variable such that }.(-)F(-) is the

(Hint: Cf. IV.4.19.) 8 Show, with the hypotheses and notation of Exercise 6, that if

b is in L,(—oo, +00), then |b(t)[=-"|F(t)]"dt < oo. 9 Let A be a real function of a real

variable such that }.(-)F(-) is the

**Fourier**transform of a function in L1(- oo, + oo) ...Page 1075

15 Show that there exists a function / in L1(——0o, +00) for which the family of

functions 1 +4 fA(a:) = —f F(t)e"“'dt, 2r: _A F denoting the

fails to satisfy the inequality sup I |fA(z)[dar < 00. .4>o 16 Show that not every ...

15 Show that there exists a function / in L1(——0o, +00) for which the family of

functions 1 +4 fA(a:) = —f F(t)e"“'dt, 2r: _A F denoting the

**Fourier**transform of f,fails to satisfy the inequality sup I |fA(z)[dar < 00. .4>o 16 Show that not every ...

Page 1178

If G is a function with values in the Hilbert sequence space I2, whose nth

component has the

cu/>dy; equivalently, .Z'G is the scalar-valued function whose

...

If G is a function with values in the Hilbert sequence space I2, whose nth

component has the

**Fourier**transform §,,(E), then put <62) (Yew) = fff_f'K<w—y> -cu/>dy; equivalently, .Z'G is the scalar-valued function whose

**Fourier**transform is...

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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