The Cayley transform shows that is isomorphic to the group " H " " D " of biholomorphisms of the bounded domain " D ".
12.
Existence of the solution and spectral properties then follow from the theory of compact operators; in particular, an elliptic boundary value problem on a bounded domain has infinitely many isolated eigenvalues.
13.
This is the special case for of the Jordan algebraic result, explained below, which asserts that the Cayley transform and its inverse establish a bijection between the bounded domain and the tube domain.
14.
This does not give a 1 : 1 correspondence between homogeneous bounded domains and " j "-algebras, because a homogeneous bounded domain can have several different Lie groups acting transitively on it.
15.
This does not give a 1 : 1 correspondence between homogeneous bounded domains and " j "-algebras, because a homogeneous bounded domain can have several different Lie groups acting transitively on it.
16.
And we can be certain that this continued fraction converges uniformly on every bounded domain in the complex plane because it is equivalent to the power series for " e " " z ".
17.
He asked whether all bounded homogeneous domains are symmetric . answered Cartan's question by finding a Siegel domain of type 2 in 4 dimensions that is homogeneous and biholomorphic to a bounded domain but not symmetric.
18.
A common question is to estimate the mean sojourn time of a particle diffusing in a bounded domain \ Omega before it escapes through a small absorbing window \ partial \ Omega _ a in its boundary \ partial \ Omega.
19.
The formulation is the following : a Brownian particle ( ion, molecule, or protein ) is confined to a bounded domain ( a compartment or a cell ) by a reflecting boundary, except for a small window through which it can escape.
20.
Let \ Omega be a bounded domain in \ mathbb { R } ^ d with a sufficiently regular boundary \ Gamma, let " h " be a function on \ Gamma, and let x be a point inside \ Omega.
