Linear Operators: General theory |
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Page 741
... equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc . Nat . Acad ...
... equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc . Nat . Acad ...
Page 763
... equation . Amer . J. Math . 71 , 206-213 ( 1949 ) . On the location of spectra of wave equations . Amer . J. Math . 71 , 214–217 ( 1949 ) . On the Laplace - Fourier transcendents . Amer . J. Math . 71 , 367–372 ( 1949 ) . 10 ...
... equation . Amer . J. Math . 71 , 206-213 ( 1949 ) . On the location of spectra of wave equations . Amer . J. Math . 71 , 214–217 ( 1949 ) . On the Laplace - Fourier transcendents . Amer . J. Math . 71 , 367–372 ( 1949 ) . 10 ...
Page 779
... equation with small quantum numbers . Phys . Rev. 75 , 1573-1578 ( 1949 ) . The expansion problem in the theory of ... equation . Proc . Nat . Acad . Sci . U.S.A. 35 , 190–193 ( 1949 ) . On self - adjoint differential equations of the ...
... equation with small quantum numbers . Phys . Rev. 75 , 1573-1578 ( 1949 ) . The expansion problem in the theory of ... equation . Proc . Nat . Acad . Sci . U.S.A. 35 , 190–193 ( 1949 ) . On self - adjoint differential equations of the ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ