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Some Useful Solution Representations
Zeros and Boundedness of Solutions
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angular and radial arbitrary constant Bocher's boundary conditions 4.2 boundary-value problem bounded BOUNDEDNESS Ca,b Cartesian coordinate systems Catholic University coefficient matrices comparison theorems continuous function continuous on a,b corresponding CT)dt d/dt differential equation dissertation exist an infinite existence of real Existence Theorem expansion theory first-order formal self-adjointness fundamental matrix given t-interval Given the system hypotheses identity matrix increasingly rapid oscillation infinite number integrals linear homogeneous linear system linearly independent Lukacs and Dr matrix-vec matrix-vector mixed boundary condition mn x mn Mod(rf Mx(a non-self-adjoint nondecreasing number of eigenvalues number of real ordering the eigenvalues P^Ct polar Professor Eugene Lukacs Proof quadratic forms connected real and continuous real eigenfunctions real eigenvalues Riccati equation satisfies 4.7 Saworotnow scalar solution representations spherical coordinates Sturm Sturmian and mixed Sturmian boundary conditions sufficient condition symmetric system x Theorem 17 Theorem 20 tions uniformly convergent UNIVERSITY OF AMERICA ution vector solution XA(t zeros