Introductory Linear Operator Theory

摘要: In this chapter we apply concepts of functional analysis, especially those related to Hilbert and Banach spaces, introduce basic operator theory relevant applied electromagnetics. We begin with the definition a linear provide examples common operators that arise in physical problems. next define functionals as special class operators. Linear occur quite often electromagnetics are very useful theoretical investigations formulating problems be solved numerically. addition, concept functional, conjunction Riesz representation theorem, gives an appropriate motivation for introducing important adjoint operator. Next, self-adjoint is discussed, well broader category normal will see later operators, compact have nice mathematical properties can usefully exploited. Definite then which themselves contained within or symmetric lead new notion convergence. Compact introduced, both at function sequence (infinite matrix) levels, from mathematics provided.