Mathematical Constraint on Functions with Continuous Second Partial Derivatives
Quantum Physics
2015-05-18 v4
Abstract
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations r' and retarded times t'<t, provided that the function vanishes at infinity and has continuous second partial derivatives. Functions of this kind occur in many areas of physics and it seems somewhat surprising that they are constrained in this way.
Keywords
Cite
@article{arxiv.1004.1393,
title = {Mathematical Constraint on Functions with Continuous Second Partial Derivatives},
author = {J. D. Franson},
journal= {arXiv preprint arXiv:1004.1393},
year = {2015}
}
Comments
10 pages, 6 figures