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abelian abelian groups abstract algorithm analysis analytic applications approximation asymptotic automorphisms Banach space boundary bounded C*-algebra California characterization coefficients commutative ring compact complex conjecture construction convergence convex countable curvature defined denote differential equations dimensional domain eigenvalues elements equivalent exists extension field finite formula functions geometry given graph Hilbert Hilbert space homeomorphism ideal infinite integral invariant inverse isomorphic lattice Lie algebra Lie group linear manifold Math Mathematical matrix method minimal modules nonlinear normal subgroup obtained October 17 October 31 operator orthogonal polynomials paper polynomials Preliminary report prime problem proof properties prove quadratic random Received August Received December Received January Received June Received November Received October 17 Received September representation ring SAHARON SHELAH satisfies semigroup sequence singular solutions stability stochastic structure subgroup subset symmetric Texas Theorem theory topological topological group transform University vector zero