Pointwise Solutions Research Articles

Quasiperiodic pointwise solutions of the periodic, time-dependent Schrödinger equation

For Hamiltonians periodic in time, we obtain under certain assumptions a condition which is necessary and sufficient for the existence of quasiperiodic pointwise solutions to the Schrödinger equation. Orthonormality and completeness of these functions in L2(Rn) are investigated, and the time-displacement operator is considered as a sum of quasiperiodic terms.

Weyl's Lemma for Pointwise Solutions of Elliptic Equations

Weyl's Lemma for Pointwise Solutions of Elliptic Equations

Removable Sets for Pointwise Solutions of Elliptic Partial Differential Equations

Removable Sets for Pointwise Solutions of Elliptic Partial Differential Equations

Removable sets for pointwise solutions of elliptic partial differential equations

We prove that dense sets of zero newtonian capacity are removable for bounded generalized pointwise solutions of second order elliptic equations.

Removable Sets for Pointwise Solutions of the Generalized Cauchy-Riemann Equations

We shall operate in N-dimensional euclidean space EN, N _ 2, and use the following notation. x = (xI, *.* , XN) and B(x, r) = the open N-ball with center x and radius r. Also, we shall adopt the convention that if P(x) is a polynomial of degree less than zero, then P(x) is identically zero. We say the function f(x) is in T'(x,), a c N, if f(x) is in L' in a neighborhood of the point x0, and if there is a polynomial P(x) of degree strictly less than a such that

Characteristic Planes and Pointwise Solutions of the Heat Equation

Characteristic Planes and Pointwise Solutions of the Heat Equation