This text investigates the foundational definitions, theorems, and methodologies governing the theory of Birkhoff interpolation by polynomials. The author, G. G. Lorentz, synthesizes decades of research to provide a unified framework for understanding how interpolation techniques function within approximation theory. By consolidating disparate developments, the work serves as a comprehensive reference for the mathematical principles underlying lacunary interpolation and spline-based systems.

Experts recognize this volume as a foundational reference for researchers and students specializing in numerical analysis and approximation theory. Readers frequently note the technical density of the prose, which assumes a high level of mathematical proficiency from its audience.