This book is a tribute to the achievements of Ilya Spitkovsky in operator theory, pseudo-differential and integral equations, factorization theory and many other related topics.

Ilya Spitkovsky started his career under the guidance of Mark Krein in Odessa, Ukraine. During these years, Ilya's rigorous and clear style of doing mathematics matured. Since 1990 Ilya Spitkovsky has been a professor of mathematics at the College of William and Mary in Williamsburg, Virginia, where he has taught a wide range of courses, including linear algebra, real, complex, and functional analysis. He has authored more than 300 publications, including four research monographs, and edited eight books of proceedings. Ilya Spitkovsky is currently a member of the editorial board of five international journals. Since 2013 he is a professor of the Division of Science and Mathematics New York University Abu Dhabi, UAE.

With this volume, the authors of the articles join the large family of people who congratulate Ilya Spitkovsky on his anniversary. It is their wish that the contributions in this volume offer inspiring insights to researchers working in these fields.

Sergei Rogosin graduated from the Department of Mathematics, Belarusian State University, Minsk, Belarus, in 1974, and got his PhD at Belarusian State University, Minsk, Belarus, in 1980 (scientific adviser academician F.D. Gakhov). He is the author of 4 monographs and more than 200 research publications and editor of several books of proceedings.

- Ilya Spitkovsky 70.- Ilya Spitkovsky's pioneering work on massive local spectra of Toeplitz operators.- The Reciprocal Schur Inequality.- On Iterative Procedure for a Vectorial Wiener-Hopf Problem with Oscillating Terms.- A direct proof of an inversion formula for Bezoutians.- A Numerical Algorithm for Matrix Spectral Factorization on the Real Line.- On topological aspects of numerical range.- On dilations of Fourier multipliers on weighted Lebesgue spaces.- On the Algebras of Wiener-Hopf Operators with Continuous Symbols Acting on Some Banach Function Spaces.- Algebras of Convolution Type Operators with Piecewise Quasicontinuous and Piecewise Slowly Oscillating Data onWeighted Lebesgue Spaces.- On solution to Riemann problem in logarithmic cases.- Operator Projective Line and Its Transformations.- Fredholm Determinants, Continued Fractions, Jost and Evans Functions for a Jacobi Matrix Associated with the 2D-Euler Equations.- Factorization of Partly Rational Matrix-Functions and its Application to the Solution of R-linear Conjugation Problem.