Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1051
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae Sgn P ( x ) dx = √gn 4 ( Ux ) dx , -n Sgn P ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , E which are valid for every ...
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae Sgn P ( x ) dx = √gn 4 ( Ux ) dx , -n Sgn P ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , E which are valid for every ...
Page 1347
... evident advantage that it makes σ¡ ( • , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
... evident advantage that it makes σ¡ ( • , λ ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
Page 1756
... evident consequence of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the existence of the function I to the proof of the following statement . ( ii ) For each r > 0 and p≥1 , there exists a function 7 ...
... evident consequence of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the existence of the function I to the proof of the following statement . ( ii ) For each r > 0 and p≥1 , there exists a function 7 ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero