A new proof of Poltoratskii's theorem

We provide a new simple proof to the celebrated theorem of Poltoratskii concerning ratios of Borel transforms of measures. That is, we show that for any complex Borel measure μ on and any a.e. w.r.t. μ_sing, where μ_sing is the part of μ which is singular with respect to Lebesgue measure and F denotes a Borel transform, namely, and F_μ(z)=∫(x−z)⁻¹dμ(x).     

A new proof of Mayer''s theorem

This paper gives a new proof of Mayer's theorem concerning the convergence of powers of an interval matrix.     

A new proof and generalizations of Gearhart's theorem

Let be a Hilbert space, let be the space of almost periodic functions from to , and let be a closed densely defined linear operator on . For a closed subset , let be the subspace of consisting of functions with spectrum contained in . We prove that the following properties are equivalent: (i) for every function there exists a unique mild solution of equation ; (ii) and . The case yields a new proof of the well-known Gearhart's spectral mapping theorem.

     

A new proof of the Caffarelli-Kohn-Nirenberg theorem

Here we give a self-contained new proof of the partial regularity theorems for solutions of incompressible Navier-Stokes equations in three spatial dimensions. These results were originally due to Scheffer and Caffarelli, Kohn, and Nirenberg. Our proof is much more direct and simpler. © 1998 John Wiley & Sons, Inc.     

A new proof of the Eilenberg-Zilber-Cartier theorem

Let T and D denote respectively the functors which assign to every semi-simplicial double object in an abelian category with infinite direct sums, the total and the diagonal complex. The idea of the proof of the theorem in the title of this note is to show that H_nT and H_nD are left-satellites and that HT=HD. A proof of this theorem was first given in[2].The author is a recipient of an Alexander von Humboldt fellowship at the Department of Mathematics of the University of Heidelberg.     

A new proof of the Abhyankar-Moh-Suzuki theorem

We give a new proof of the famous result that any two embeddings of the affine lineA ¹ inA ² are equivalent by an automorphism ofA ². We also prove that iff(X,Y) is a polynomial overC with one place at infinity, then for every C,f– also has one place at infinity. The proof uses basic results about algebraic surfaces.     

A new proof of the Gitik-Shelah theorem

A purely combinatorial proof of a recent result of M. Gitik and S. Shelah is presented.     

A new proof of the Solomon-Tits theorem

We give a new proof of the Solomon-Tits Theorem which asserts that the Tits building of a finite group of Lie type has the homotopy type of a bouquet of spheres.

     

A new proof of the Maurey-Pisier theorem

In this paper we give a new proof of the Maurey-Pisier theorem about the finite representation ofl _pE andl _qE in any infinite dimensional Banach spaceE.     

A new proof of Doob-Meyer decomposition theorem

In this Note, we use backward stochastic differential equations (BSDEs) to prove the famous Doob-Meyer decomposition theorem for supermartingales.     

A new proof of Masser's vanishing theorem

We give a simple proof of Masser's vanishing theorem, which is important in investigating the algebraic independence of the values of Mahler functions.