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abelian abelian groups abstract algorithm 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 holomorphic homeomorphism homotopy ideal infinite integer integral invariant inverse isomorphic lattice Lie algebra Lie group linear manifold Math Mathematics matrix matroids maximal method minimal modules nonlinear normal subgroup obtained October 17 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 topology transform University vector zero