ABSTRACT
Moment theory, orthogonal functions, linear functionals and integral transforms are found in many parts of twentieth century mathematics and its applications in mathematical physics, chemistry, statistics and engineering. The analytic theory of continued fractions plays a central role in both the origin and the development of these closely related topics. Moment theory has been developed by using tools from different mathematical areas including: (a) continued fractions, (b) orthogonal polynomials (and Laurent polynomials) and (c) functional analysis. The present paper is an expository survey of the theory of regular, strong Hamburger moment problems developed by means of continued fractions called APT-fractions (alternating, positiveterm continued fractions). Although connections with orthogonal Laurent polynomials are pointed out, no essential use is made of orthogonal functions or of quadrature formulas.
