## Linear Operators: Spectral operators |

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Page 1070

symbol K, for a

same way that there exists another

du < K, J, Q,0)"u(do). Since by Theorem 11 there exists a

Ko ...

symbol K, for a

**constant**depending only on e and (21). We may conclude in thesame way that there exists another

**constant**Ke such that (3) |... visu)-(K, wo)(u)"du < K, J, Q,0)"u(do). Since by Theorem 11 there exists a

**constant**K, such that |Ko ...

Page 1154

Since the product group Roo) = Rx R is locally compact and G-compact, it has a

Haar measure 2°) defined on its Borel field X (*) and what we shall prove is that

for some

...

Since the product group Roo) = Rx R is locally compact and G-compact, it has a

Haar measure 2°) defined on its Borel field X (*) and what we shall prove is that

for some

**constant**c, (R(*), X(*), A(2)) = c(R, X, A)x (R, 2, Z). Since it is clear that X*...

Page 1176

Subtracting a suitable

without loss of generality that k,(– 00) = 0 for each n; here we have used the

uniform boundedness of the functions k, and of their variations to conclude that

the ...

Subtracting a suitable

**constant**c, from each of the functions k, we may supposewithout loss of generality that k,(– 00) = 0 for each n; here we have used the

uniform boundedness of the functions k, and of their variations to conclude that

the ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero