Applications of biorthogonal systems of functions to the theory of integral equations
Anna Johnson Pell · Transactions of the American Mathematical Society · 1911
In this paper we give a sufficient colldition that the characteristic numbers of an unsymmetric kernel exist and be real, and prove the expansibility of arbitrary functions in terms of the corresponding characteristic functions. This sufficient condition is stated in terms of a functional transformationt T(f) defined by eertain general properties (§1), and for the special case T(f) _f we obtain the known theory of the orthogonal integral equations. The method employed is that of infinitely many variables and is based to some extent on an earlier paper.t However, the present paper, with the exeeption of a few footnotes, can be read independently of (I) if Theorems 20 and 8 which are here stated in §1 are accepted; and if the suggestion in Remark 1 of §1 is carried out, the only reference to (I) that is necessary is Theorem 20.