Regularity of functions smooth along foliations, and elliptic regularity

Critical Regularity of Invariant Foliations

:D AEDF .=G . The spectrum H $ I(KJEL of its complexification is called the Mather spectrum [M]. Anosov showed that and , called the unstable and stable bundles, are Hölder continuous. One an give lower bounds for attainable values of the Hölder exponent in terms of contraction and expansion rates of ! . Optimal estimates and reasons for wanting them are given in [H2, HW]. They are not exceeded...

Hh Older Regularity of Horocycle Foliations

Strong Topological Regularity and Weak Regularity of Banach Algebras

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

Elliptic regularity and Monopoles Richard

Pseudodifferential Operators and Elliptic Regularity

Theorem 1. Let M be a compact manifold, E and F be two (smooth) vector bundles over M , and P : C∞(M ;E) → C∞(M ;F ) be a differential operator (with smooth coefficients) of order n. Assume that P is elliptic, in the sense defined in the next section. Then: 1. The operator P (or rather its relevant extension) is Fredholm W n 2 (M ;E)→ L(M ;F ). Here W n 2 is a Sobolev space (introduced below). ...