Eigenvalues and Eigenfunctions of a Class of Potential Operators in the Plane |
Other editions - View all
Common terms and phrases
analytic annulus Borel measures boundary component bounded convergence bounded sets c²(D characteristic convergence compact operator compact set compact subsets conclude constant continuous extension continuous with respect convergence theorem D₁ D₂ defined definition denote dielectric Green's function disc of radius domain of given dominated convergence theorem double-layer potentials eigen eigenfunction eigenfunctions associated eigenvalue and associated extremal problem feL D finite follows given transfinite diameter Green's identity harmonic Hence implies kernel L¹(D monotonicity Moreover neighborhood o(p² pointwise and boundedly proof r₁ r₂ satisfies Schiffer Schwarz inequality sets of L²(D simply connected slit plane solution spectrum subharmonic sufficiently small superharmonic Theorem 2.4 transfinite diameter uniform convergence uniformly unique negative eigenvalue vanish identically vanishes at infinity variational ατ πλ дг др др