Gian-Carlo Rota on analysis and probability : selected papers and commentaries [edited by] Jean Dhombres, Joseph P.S. Kung and Norton Starr.

Gian-Carlo Rota on his work in analysis --
Reminiscences of Gian-Carlo Rota / Peter Duren --
Gian-Carlo Rota (1932-1999) / Jacob T. Schwartz --

Ch. 1. Differential Operators.
Reprinted papers--
Extension theory of differential operators I--
On the completeness of Sturm-Liouville expansions / Garrett Birkhoff--
On the spectra of singular boundary value problems--
Articles--
Bernd Schultze, Rota's work on differential operators--
Norton Starr, Sturm-Liouville expansions--

Ch. 2. Theory of Linear Operators:
Reprinted papers--
Note on the invariant subspaces of linear operators--
On models for linear operators--
A note on the joint spectral radius (with W. Gilbert Strang)--
Multiplicative extensions of positive linear operators--
Dilations of positive operators--
A method for the study of positive operators--
Review. Nelson Dunford and Jacob T Schwartz, Linear Operators. Part II. Spectral Theory--
Articles, James Rovnyak, Invariant subspaces and models for linear operators--
H. H. Schaefer and X. D. Zhang, Gian-Carlo Rota's work on positive operators--
Gilbert Strang, The joint spectral radus--

Ch 3. Reynolds Operators
Reprinted papers, On the representation of averaging operators--
Spectral theory of smoothing operators--
Endomorphismes de Reynolds et theorie ergodique--
Representation des operateurs de Reynolds--
Une generalisation de I'esperance mathematique conditionnelle, qui se presente dans la theorie statistique de la turbulence--
On Reynolds operators in finite-dimensional algebras (with Martin Billik)--
On the passage from the Navier-Stokes equations to the Reynolds equations--
Reynolds operators--
Article/ Jean Dhombres, Reynolds and averaging operators--

Ch 4. Ergodic Theory
Reprinted papers/ Une theorie unifree des martingales et des moyennes ergodiques--
An "alternaierende Verfahren" for general positive operators--
On the classification of periodic flows--
On the maximal ergodic theorem for Abel-limits--
A limit theorem for the time-dependent evolution equation--
Frobenius reciprocity in ergodic theory (with Kenneth Lange and Arlan Ramssy)--
Articles/Arlan Ramsay, Frobenius recipocity--
M. M. Rao, A unified theory for ergodic and martingale theorems--
Norton Starr, A bel ergodic theory--
Radu Zaharopol, An "alternierende Varfahren" I--
Norton Starr, An "alte4nierende Verfahren" II--

Ch. 5. Inequalities
Reprinted paper/ On the inequality (with Robert R. Kallman)
Article/W.N. Everitt and A. Zettl, The Kallman-Rota inequality; a survey--

Ch 6. Geometric Probability and Profinite Combinatorics
Reprinted papers/Totally invariant set functions of polynomial type (with Beifang Chen)--
A continuous analogue of Sperner's theorem (with Daniel A. Klain)--
A stochastic interpretation of the Riemann zeta function (with Kenneth S. Alexander and Kenneth Baclawski)--
An example of profinite combinatorics--

Ch. 7. Probability Theory
Reprinted papers/A measure theoretic approach to logical quantification (with David P. Ellerman)--
Stochastic integrals: a combinatorial approach (with Timothy C. Wallstrom)--
Probability set functions (with William J. Bruno and David C. Torney)--
On the combinatorics of cumulants (with Jianhong Shen)--
Articles/Joseph P. S. Kung, Rota's foundations of probability theory--
David C. Torney, Cumulants and probability set functions--

Gian-Carlo Rota was one of those rare mathematicians who made major contributions to several areas of mathematics. This book presents his papers on differential equations, operator theory, ergodic theory, and other subjects.