A general coefficient theorem

The General Coefficient Theorem and Certain Applications

Teichmüller was the first person to point out explicitly the connection between quadratic differentials and the solutions of certain extremal problems in Function Theory. He enunciated the principle that if a point is required to be fixed the quadratic differential will have a simple pole there, if in addition fixed values are required for the first n derivatives of competing functions the quad...

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

A Universal Coefficient Theorem for Gauss’s Lemma

We shall prove a version of Gauß’s Lemma that recursively constructs polynomials {ck}k=0,...,m+n in Z[ai, Ai, bj , Bj ]i=0,...,m, j=0,...,n, of degree at most ( m+n n ) , such that whenever ∑ k CkX k = ∑ i AiX i · ∑ j BjX j and 1 = ∑

A General Correlation Theorem

A general ballot theorem

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.