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Then the change of variables, or area formula holds for f provided removing from counting into the multiplicity function the set where f is not approximately H¨ older continuous1.

This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0.. The method of power series

We present sufficient conditions for the existence of solutions to Neu- mann and periodic boundary-value problems for some class of quasilinear ordinary differential equations.. We

As an application, in Section 5 we will use the former mirror coupling to give a unifying proof of Chavel’s conjecture on the domain monotonicity of the Neumann heat kernel for

In Section 13, we discuss flagged Schur polynomials, vexillary and dominant permutations, and give a simple formula for the polynomials D w , for 312-avoiding permutations.. In

Analogs of this theorem were proved by Roitberg for nonregular elliptic boundary- value problems and for general elliptic systems of differential equations, the mod- ified scale of

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

Correspondingly, the limiting sequence of metric spaces has a surpris- ingly simple description as a collection of random real trees (given below) in which certain pairs of