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abelian abstract algorithm analysis analytic applications approximation asymptotic Banach Banach spaces boundary bounded C*-algebra coefficients cohomology College compact complex Computer conjecture construction continuous functions convergence convex curvature curves defined denote Department of Mathematics differential equations dimension dimensional discuss domain dynamical eigenvalues embedding existence field finite functions fundamental group geometry given graphs Hilbert space holomorphic homeomorphism homotopy Hopf algebra ideal inequalities infinite integer integral invariant inverse isomorphic lattice Lie algebra Lie group linear manifolds matrix mean curvature method metric minimal modules nonlinear obtained October 9 operator paper parameter polynomial Preliminary report prime problem properties prove Radon transform random Received August Received December Received January Received July 29 Received October Received September representation ring semigroup sequence singular solutions space Sponsored stochastic structure subgroup subset surface symmetric theorem theory tilings topological topology transform variables vector zero