Recent Trends in Operator Theory and Partial Differential Equations : The Roland Duduchava Anniversary Volume This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz Wiener Hopf and pseudodifferential operators boundary value problems operator theory approximation theory and reflects the broad spectrum of Roland Duduchavas research. The book is addressed to a wide audience of pure and applied mathematicians Roland Duduchava The Duduchava Roch formula Convolution Type Operators with Symmetry in Bessel Potential Spaces On Symmetries of the Feinberg Zee Random Hopping Matrix Inequalities of Babuška Aziz and Friedrichs Velte for differential forms High Frequency Oscillations of first Eigenmodes in Axisymmetric shells as the thickness tends to zero Kernels of Wiener Hopf plus Hankel operators with matching generating functions Spline Galerkin methods for the double layer potential equations on contours with corners C* algebras of Bergman Type Operators with Piecewise Continuous Coefficients over Bounded Polygonal Domains Solvability and Lyapunov stability of a two component system of generalized Poisson Nernst Planck equations A local uniqueness result for a quasi linear heat transmission problem in a periodic two phase dilute composite The method of potential operators for anisotropic Helmholtz operators on domains with smooth unbounded boundaries Gabor Analysis for Schrödinger Equations and Propagation of Singularities Commutative algebras of Toeplitz operators on a Siegel domain associated with the nilpotent group of its biholomorphisms