This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions.

There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particular, certain aspects of Gesztesy's work. The remaining seventeen papers contain original research results in diverse areas reflecting his interests. The topics of these papers range from stochastic differential equations; operators on graphs; elliptic partial differential equations; Sturm-Liouville, Jacobi, and CMV operators; semigroups; to inverse problems.

Readership

Graduate students and research mathematicians interested in spectral theory and mathematical physics.

Table of Contents

• S. Albeverio, E. Mastrogiacomo, and L. Di Persio -- Invaraint measures for stochastic differential equations on networks
• D. Bollé, F. L. Metz, and I. Neri -- On the spectra of large sparse graphs with cycles
• K. Brewster, D. Mitrea, I. Mitrea, and M. Mitrea -- Jones' extension operator on Sobolev spaces with partially vanishing traces
• B. M. Brown, W. D. Evans, and I. G. Wood -- Some spectral properties of rooms and passages domains and their skeletons
• J. S. Christiansen, B. Simon, and M. Zinchenko -- Finite gap Jacobi matrices: A review
• P. Exner -- Momentum operators on graphs
• G. Fragnelli, G. R. Goldstein, J. A. Goldstein, and S. Romanelli -- Asymptotic parabolicity for strongly damped wave equations
• A. Gomilko and Y. Tomilov -- On rates in Euler's formula for \(C_9\)-semigroups
• H. Grosse and R. Wulkenhaar -- Construction of a noncommutative quantum field theory
• K. Grunert, H. Holden, and X. Raynaud -- Periodic conservative solutions for the two-component Camassa-Holm system
• G. A. Hagedorn -- A minimal uncertainty product for one-dimensional semiclassical wave packets
• E. M. Harrell, II and M. L. Wong -- On a transformation of Bohl and its discrete analogue
• C. K. R. T. Jones, Y. Latushkin, and R. Marangell -- The Morse and Maslov indices for matrix Hill's equations
• A. Kostenko and M. Malamud -- 1-D Schrödinger operators with local point interactions: A review
• Y. I. Lyubarskii and V. A. Marchenko -- Inverse problem for small oscillations
• K. A. Makarov and E. Tsekanovskiĭ -- On the Weyl-Titchmarsh and Livšic functions
• R. Shterenberg, R. Weikard, and M. Zinchenko -- Stability for the inverse resonance problem for the CMV operator
• F. A. Sukochev -- On a conjecture of A. Bikchentaev
• G. Teschl and K. Unterkofler -- Spectral theory as influenced by Fritz Gesztesy
• M. Ünal and A. Zafer -- Prescribed asymptotic behavior for nonlinear second-order dynamic equations