Consider the differential equation y 0 = F(x, y). We determine weakest possible upper bound on |F(x, y) − z)| which guarantees that this has for all initial values a unique solution, exists globally.

Nous étudions les sommes des valeurs propres opérateurs de Hecke formes paraboliques Hecke–Maass pour le groupe SL(n,ℤ) avec n≥3 quelconque, sur intervalles courts d’une certaine longueur, en admettant l’hypothèse Lindelöf généralisée et une estimation l’exposant direction la conjecture Ramanujan–Petersson, un peu plus forte que celle qui est actuellement connue. En particulier, dans cette situ...

Maximum principles are among the most powerful and widely used analytic tools in the study of second-order linear and nonlinear elliptic and parabolic equations. They enable us to obtain valuable information about (real valued) solutions of differential equations and inequalities (such as a priori pointwise estimates, and uniqueness and stability results) without the need to know in advance the...

We show that every completely regular frame has a P -frame re‡ection. The proof is straightforward in the case of a Lindelöf frame, but more complicated in the general case. The chief obstacle to a simple proof is the important fact that a quotient of a P -frame need not be a P -frame, and we give an example of this. Our proof of the existence of the P -frame re‡ection in the general case is it...

We use subsequence and moving average ergodic theorems applied to Boole's transformation its variants their invariant measures on the real line give new characterisations of Lindelöf Hypothesis Riemann Hypothesis. These ideas are then used study value distribution Dirichlet L-functions, zeta functions Dedekind, Hurwitz derivatives. This builds earlier work R. L. Adler B. Weiss, M. Lifshits Webe...

In this paper we introduce, via a Phragmén-Lindelöf type theorem, maximal plurisubharmonic function in strongly pseudoconvex domain. We call such the pluricomplex Poisson kernel because it shares many properties with classical of unit disc. particular, show that is continuous, zero on boundary except at one point where has non-tangential simple pole, and reproduces pluriharmonic functions. also...