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Page 505
... equation that x * ( s ) = x * ( s ) for u - almost all s in S. Equation ( ii ) holds for æ 。 and xo therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , E ...
... equation that x * ( s ) = x * ( s ) for u - almost all s in S. Equation ( ii ) holds for æ 。 and xo therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , E ...
Page 564
... equation y ' = Ty where T is the matrix of Exercise 5 . The next ten exercises refer to the stability theory of systems of n linear homogeneous differential equations , dy ( t ) dt = A ( t ) y . Here A ( t ) = ( a ,, ( t ) ) is an nxn ...
... equation y ' = Ty where T is the matrix of Exercise 5 . The next ten exercises refer to the stability theory of systems of n linear homogeneous differential equations , dy ( t ) dt = A ( t ) y . Here A ( t ) = ( a ,, ( t ) ) is an nxn ...
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. Oscillatory ...
... 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. Oscillatory ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ