Calculus For Differential Operators Research Articles

Boundary Value Problems at Infinite Genus

Boundary value problems are formulated on infinite-genus surfaces. These are solved for a variety of boundary conditions. The symbol calculus for differential operators is developed further for solution of parabolic differential equations at infinite genus.

Bounded H ∞-Calculus for Differential Operators on Conic Manifolds with Boundary

We prove the existence of a bounded H ∞-calculus in weighted L p -Sobolev spaces for a closed extension A T of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent (λ − A T )−1 exists in a sector Λ ⊂ ℂ and has a certain pseudodifferential structure that we describe. In case A T is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem . Examples concern the Dirichlet and Neumann Laplacians.

Differential algebra (contravariant analytic methods in differential geometry)

The problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.

Joseph Fourier's Anticipation of Linear Programming

The name of Joseph Fourier (1768-1830) is largely associated with the mathematical analysis of heat diffusion and methods of solving partial differential equations by means of Fourier series, Fourier integrals and the calculus of differential operators. But his interests in mathematics encompassed other fields also, and one of his achievements was to create singlehanded a basic theory of linear programming.

Joseph Fourier's Anticipation of Linear Programming

The name of Joseph Fourier (1768-1830) is largely associated with the mathematical analysis of heat diffusion and methods of solving partial differential equations by means of Fourier series, Fourier integrals and the calculus of differential operators. But his interests in mathematics encompassed other fields also, and one of his achievements was to create singlehanded a basic theory of linear programming.