Distributions and Operators

Distributions and derivatives. - Motivation and overview. - Function spaces and approximation. - Distributions. Examples and rules of calculus. - Extensions and applications. - Realizations and Sobolev spaces. - Fourier transformation of distributions. - Applications to differential operators. The Sobolev theorem. - Pseudodifferential operators. - Pseudodifferential operators on open sets. - Pseudodifferential operators on manifolds index of elliptic operators. - Boundary value problems. - Boundary value problems in a constant-coefficient case. - Pseudodifferential boundary operators. - Pseudodifferential methods for boundary value problems. - Topics on Hilbert space operators. - Unbounded linear operators. - Families of extensions. - Semigroups of operators. Language: English