Linear Operators: Spectral theory |
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Page 1248
... called the initial domain of P and PM ( = P§ ) is called the final domain of P. = 5 LEMMA . A bounded linear operator P in Hilbert space is a partial isometry if and only if P * P is a projection . In this case PP * is also a projection ...
... called the initial domain of P and PM ( = P§ ) is called the final domain of P. = 5 LEMMA . A bounded linear operator P in Hilbert space is a partial isometry if and only if P * P is a projection . In this case PP * is also a projection ...
Page 1297
... called a boundary condition for T. A set of boundary conditions B ̧ ( f ) = 0 , i = 1 , . . . , k , is called stronger than a set C , ( f ) 1 , ... , m , if each C , is a linear combination of the B ,. Two sets of boundary conditions ...
... called a boundary condition for T. A set of boundary conditions B ̧ ( f ) = 0 , i = 1 , . . . , k , is called stronger than a set C , ( f ) 1 , ... , m , if each C , is a linear combination of the B ,. Two sets of boundary conditions ...
Page 1432
... called the order of the singularity of equation [ * ] at zero . If v = 0 , there is no singularity at all , and zero is called a regular point of the differential equation . If v = 1 , the singularity of equation [ * ] at zero is called ...
... called the order of the singularity of equation [ * ] at zero . If v = 0 , there is no singularity at all , and zero is called a regular point of the differential equation . If v = 1 , the singularity of equation [ * ] at zero is called ...
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