A remark on a mean value theorem of Alexander Weinstein in Generalized Axially Symmetric Potential Theory

Generalized Axially Symmetric Potential Theory

A Mean Value Theorem on Bounded Symmetric Domains

Let Ω be a Cartan domain of rank r and genus p and Bν , ν > p−1, the Berezin transform on Ω; the number Bνf(z) can be interpreted as a certain invariant-mean-value of a function f around z. We show that a Lebesgue integrable function satisfying f = Bνf = Bν+1f = · · · = Bν+rf , ν ≥ p, must be M-harmonic. In a sense, this result is reminiscent of Delsarte’s two-radius mean-value theorem for ordi...

On Generalized Flett's Mean Value Theorem

We present a new proof of generalized Flett’s mean value theorem due to Pawlikowska (from 1999) using only the original Flett’s mean value theorem. Also, a Trahan-type condition is established in general case.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on the equations of axially symmetric gravitational fields

A local theorem of existence and uniqueness of solutions of the equations of stationary axially symmetric vacuum gravitational fields in the general theory of relativity close to the flat space solution is proved using the implicit function theorem in Banach spaces. Mathematics Subject Classification (2010). 83C10, 83C05