A Characterization for reproducing kernel Hilbert spaces
Copyright policy )A Characterization for reproducing kernel Hilbert spaces
AbstractLet G(t, s) be the Green's functions associated with N, a differential operator restricted to certain boundary conditions. Define (u, v)N = (Nu, v)L2. It is shown that the reproducing kernel Hilbert space generated by G is the same as the Hilbert-space completion with respect to ∥ · ∥N of the set of real valued functions which are in C2n and satisfy the boundary conditions. The concept of Sobolev spaces is used in the proof and examples are given.
- University of New Mexico United States
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Applied Mathematics, General theory of ordinary differential operators, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Applied Mathematics, General theory of ordinary differential operators, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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