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Thus, we see that a square function inequality much like that of (2.13) holds; this completes the proof of Rubio de Francia’s Theorem in the one- dimensional case, aside from the
We now use Theorem 2.6 to show that coherent unit actions on ABQR operads are preserved by the black square product and thus give rise to Hopf algebra structures on the free objects
Abstract. In this article we expose a proof of the Canonical Decomposi- tion Theorem of irreducible 3-manifolds along tori and annuli, also known as JSJ Theorem. This proof will
The first proof, given in Section 2, uses a decomposition of the paths under consideration, while the second proof, given in Section 3, uses the continued fraction theorem due to
The following theorem proves Schur’s congruence for scaled Legendre polynomials. The proof is identical to Wahab’s for the usual
Our proof of Theorem 2 follows by enumerating the degree sequences which fit into each of the five categories in Theorem 1 and then removing those that have been counted multiple
Section II will contain the proof of the theorem of factorization of matrix-functions and present the theorem of singular operators that are Noetherian in weighted
application of Glicksburg’s Theorem (Glicksburg, 1952) that the game form g exhibits a (mixed strategy) Nash equilibrium. We contend that local pure strategy Nash equilibria can
