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The General Problem
The Cases When p Is Identically One
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analytic apply assume Banach space boundary bounded variation canonical functions characteristic roots closed consider constant convergence convex cone convex functions convex set Corollary corresponding defined denote derivative dx dy eigenvalues element equality holds equation equivalence classes example exists extended finite Fourier Fourier series G. H. Hardy given gives Haar measure harmonic functions Hence hermitian hypermetric hypothesis implies index set inequality infinite inner product inner product space integral kernel Lemma locally compact Math matrix measure meromorphic metric space necessary and sufficient nonnegative norm obtain operator orthonormal basis poles polynomial positive numbers problem proof of Theorem prove real numbers Remark restriction result satisfies Section sequence singularity solution spline function subset subspace sufficient condition Suppose symmetric Theorem 2.2 theory tk+1 topological vector spaces transformation values variables zero