Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 909
... meaning of this phrase is given in the following definition . Here and elsewhere the symbol will be used for the direct sum of the Hilbert spaces Ha ( cf. IV.4.18 and IV.4.19 ) . The ath component of an element x in Σ will be denoted by ...
... meaning of this phrase is given in the following definition . Here and elsewhere the symbol will be used for the direct sum of the Hilbert spaces Ha ( cf. IV.4.18 and IV.4.19 ) . The ath component of an element x in Σ will be denoted by ...
Page 1280
... 7 is a formal differential operator of order n on the interval I , and ƒ e A " ( I ) , then the expression τf has a definite meaning in a very natural sense : we put ( Tf ) ( t ) = a , ( 1280 XIII.1.1 XIII . ORDINARY DIFFERENTIAL OPERATORS.
... 7 is a formal differential operator of order n on the interval I , and ƒ e A " ( I ) , then the expression τf has a definite meaning in a very natural sense : we put ( Tf ) ( t ) = a , ( 1280 XIII.1.1 XIII . ORDINARY DIFFERENTIAL OPERATORS.
Page 1648
... meaning to F for each F in D ( I ) . If , on the other hand , the operator is of order zero , i.e. , is the operation of multiplying by a function a in C ( I ) , then Definition 5 assigns a meaning to the product aF for each F in D ( I ) ...
... meaning to F for each F in D ( I ) . If , on the other hand , the operator is of order zero , i.e. , is the operation of multiplying by a function a in C ( I ) , then Definition 5 assigns a meaning to the product aF for each F in D ( I ) ...
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