Hille E., Phillips R.S. Functional Analysis and Semi-groups

American Mathematical Society, 1957. - 819 Pages.
Each Part of the book starts with a Summary, each chapter with an Orientation. The chapters are divided into sections and the sections, except for orientations, are grouped into paragraphs. Cross references are normally to sections, rarely to paragraphs. section 3.10 is the tenth section in chapter III; it belongs to §2 which is referred to as §3.2 when necessary. The page headings show the numbers of current section and paragraph, the integral part of the former is the number of the chapter. Definitions, formulas, lemmas, and theorems are numbered separately within each thus Theorem 9.4.2 is the second theorem in section.
9.4. references to the literature give the author's name followed by numerals in brackets referring to his book or paper by that number in the Bibliography at the close of the book. Such references are given in the text when needed; collected references for a whole chapter occur after the orientation to the chapter in question except for chapters with heterogeneous subject matter in which case they are given at the end of each paragraph.Chapter I. Abstract Spaces.
Chapter II. Linear Transformations.
Chapter III. Vector-valued functions.
Chapter IV. Banach algebras.
Chapter V. Analysis in a Banach algebra.
Chapter VI. Laplace integrals and binomial series.
Chapter VII. Subadditive functions.
Chapter XIII. Perturbation theory.
Chapter XIV. Adjoint theory.
Chapter XV. Operational calculus.
Chapter XVI. Spectral theory.
Chapter XVII. Holomorphic semi-qroups.
Chapter XVIII. Applications to ergodic theory.
Chapter XIX. Translations and powers.
Chapter XX. Trigonometric semi-groups.
Chapter XXI. Semi-groups in L_p.
Chapter XXII. Semi-groups in Hilbert space.
Chapter XXIII. Miscellaneous applications.
Chapter XXIV. Notes on Banach algebras.
Chapter XXV. Lie semi-Groups.
Chapter XXVI. Functions on vectors to vectors.