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THE OPERATORS OF MATHEMATICAL PHYSICS
The scalar product of functions
The concepts of operator and of functional
90 other sections not shown
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approximate solution boundary conditions Cauchy's inequality class of functions closed domain coefficients complete in energy consider construct coordinate functions corresponding defined denote derivatives differential equation Dirichlet problem displacement domain Q easily seen eigenfunctions eigenvalues eigenvalues of operator elasticity theory element equal to zero equals zero exact lower bound example exists field of definition finite energy finite norm function u(P functions satisfying functions which satisfy functions with finite given Green's formula Hence it follows Hilbert space identity Lebesgue integral linear set linearly mean method of orthogonal minimizing sequence Neumann problem non-negative obtain orthogonal projections plate positive definite possible proved quantity rigidly fixed Ritz method satisfies conditions satisfies equation satisfies the equation satisfy boundary conditions satisfy the boundary scalar product sense of convergence set of functions solution of equation subspace symmetric operator theorem tion Trefftz Un(P Un(x vanishes variable variational problem vector virtue