Linear Operators, Part 2 |
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Page 1280
... called the coefficient functions , belong to C ( I ) , and such that the function a ,, called the leading coefficient , is not zero at any point of I. If the coefficients of t are in C ( I ) , but the leading coefficient a is allowed to ...
... called the coefficient functions , belong to C ( I ) , and such that the function a ,, called the leading coefficient , is not zero at any point of I. If the coefficients of t are in C ( I ) , but the leading coefficient a is allowed to ...
Page 1297
... called stronger than a set C , ( f ) = 0 , j 1 , ... , m , if each C , is a linear combination of the B. Two sets of boundary conditions are called equivalent if each is stronger than the other . A complete set of boundary values is a ...
... called stronger than a set C , ( f ) = 0 , j 1 , ... , m , if each C , is a linear combination of the B. Two sets of boundary conditions are called equivalent if each is stronger than the other . A complete set of boundary values is a ...
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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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 deficiency indices Definition denote dense 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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero