Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

The Annals of Probability, Vol. 15, No. 3 (Jul., 1987), pp. 954-984 (31 pages) We give conditions for transience and recurrence for certain diffusion processes in the plane which "look" recurrent in ...

We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragmén-Lindelöf theorem and use Fourier ...

THE object of this work is to provide a text-book on the elements of the theory of spherical harmonics with applications to mathematical physics so far as this can be done without employing contour ...