Linear Operators: Spectral theory |
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Page 1223
... operator which will be studied in greater detail in the next chapter : the differential operator iD = i ( d / dt ) in the space L2 ( 0 , 1 ) . How are we to ... symmetric then every XII.4.1 1223 EXTENSIONS OF A SYMMETRIC TRANSFORMATION.
... operator which will be studied in greater detail in the next chapter : the differential operator iD = i ( d / dt ) in the space L2 ( 0 , 1 ) . How are we to ... symmetric then every XII.4.1 1223 EXTENSIONS OF A SYMMETRIC TRANSFORMATION.
Page 1270
... symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is ...
... symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is ...
Page 1272
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero