This is the first of three volumes presenting the works of Mark Grigorievich Kreĭn previously unavailable in English translation. Mark G. Kreĭn (Kyiv, 1907 – Odessa, 1989) was one of the foremost mathematicians of the twentieth century. His seminal contributions to functional analysis, operator theory, and related areas have had a profound and lasting influence on modern mathematics and continue to inspire contemporary research.

The present volume contains articles originally published between 1926 and 1937. It also includes a biographical essay by Inna Rikun and a complete bibliography of Kreĭn’s works.

Harry Dym † (1938–2024) was Professor Emeritus at the Weizmann Institute, Israel. He made fundamental contributions to operator theory, interpolation, systems theory, and inverse spectral problems. His research and influential monographs have shaped several generations of mathematicians.
Heinz Langer † (1935–2024) was Professor Emeritus at Technische Universität Wien, Austria. He was one of the leading mathematicians in operator theory and analysis. His pioneering work on indefinite inner product spaces, extension theory, and spectral analysis has had a profound and lasting impact on modern mathematics.
Ilya M. Spitkovsky is Professor Emeritus at New York University Abu Dhabi, United Arab Emirates. He works in operator theory, matrix analysis, numerical ranges, and linear algebra. His research has contributed to spectral theory of Toeplitz operators, Wiener-Hopf factorization, and boundary problems for analytic functions.
Christiane Tretter is Full Professor at the University of Bern, Switzerland. She is a leading expert in spectral theory and its applications, including partial differential equations, numerical analysis, and mathematical physics. Her work on operator matrices, nonlinear eigenvalue problems, and non-selfadjoint operators has significantly advanced these areas.