Vector-Valued Multibang Control of Differential Equations

Vector-valued modular forms associated to linear ordinary differential equations

We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.

Preconditioning for Vector-Valued Cahn-Hilliard Equations

A Cohomology for Vector Valued Differential Forms

A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Frölicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is functorial under local diffeomorphisms. This cohomology is determined as the direct product of the de Rham cohomology space and the graded Lie algebra of ”traceless”...

Periodic Solutions of Degenerate Differential Equations in Vector-valued Function Spaces

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...

A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus

For each irreducible module of the symmetric group SN there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N -to...