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Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Notes area operator geometric 2-rough paths Young integral
2012/4/17
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral i...
Separation of variables and explicit theta-function solution of the classical Steklov--Lyapunov systems: A geometric and algebraic geometric background
Separation of variables explicit theta-function solution
2010/4/6
The paper revises the explicit integration of the classical Steklov--Lyapunov systems via separation of variables, which was first made by F. K\"otter in 1900, but was not well understood until recent...
A geometric Kirchoff -Sobolev parametrix for the wave equation and applications
Kirchoff -Sobolev parametrix wave equation applications
2014/4/3
Together with I. Rordnianski we construct a first order, physical space, parametrix for solutions to covariant, tensorial, wave equations on a general Lorentzian manifold. The construction is entirely...