Analysis as a Tool in Mathematical Physics : In Memory of Boris Pavlov Boris Pavlov (1936 2016) to whom this volume is dedicated was a prominent specialist in analysis operator theory and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School he was one of the founders of the Leningrad School of Non self adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications” held in Stockholm Sweden in March 2016 and “Operator Theory Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg Russia in August 2016. The volume also includes water color paintings by Boris Pavlov some personal photographs as well as tributes from friends and colleagues. Part I Memorial Contributions Life and career Water colours by Boris Pavlov Family and leisure Pavlovs mathematics Part II Research Papers Singular perturbations of unbounded selfadjoint operators. Reverse approach Generic asymptotics of resonance counting function for Schrödinger point interactions Spectral clusters asymmetric spaces and boundary control for Schrodinger equation with strong singularities The second Weyl coefficient for a first order system A Lieb Thirring type inequality for magnetic Schrödinger operators with a radial symmetry Scattering matrices and Weyl functions of quasi boundary triples On the spectrum of the quantum Rabi model Scattering theory for a class of non selfadjoint extensions of symmetric operators Asymptotics of Chebyshev polynomials III. Sets saturating Szego Schiefermayr and Totitk Widom bounds Solvability and complex limit characteristics Quantization of Gaussians A resonance interaction of seismogravitational modes of tectonic plates On positivity preserving translation invariant operators in Lp(Rn)m The distribution of path lengths on directed weighted graphs Diagonalization of indenite saddle point forms Solutions of Gross Pitaevskii equation with periodic potential in dimension two The Integral Transform of N.I. Akhiezer On Gaussian random matrices coupled to the discrete Laplacian Modern results in the spectral analysis for a class of integral difference operators and application to physical processes Inverse problem for integral difference operators on graphs Quantum graph in a magnetic field and resonance states completeness On Zd symmetry of spectra of some nuclear operators Spectral monotonicity for Schrödinger operators on metric graphs Linear Operators and Operator Functions Associated with Spectral Boundary Value Problem.