Relative partition function of Coulomb plus delta interaction / Sergio Albeverio, Claudio Cacciapuoti, Mauro Spreafico -- Inequivalence of quantum Dirac fields of different masses and the underlying general structures involved / Asao Arai -- On a class of Schrödinger operators exhibiting spectral transition / Diana Barseghyan, Olga Rossi -- On the quantum mechanical three-body problem with zero-range interactions / Giulia Basti, Alessandro Teta -- On the index of meromorphic operator-valued functions and some applications / Jussi Behrndt, Fritz Gesztesy, Helge Holden, Roger Nichols -- Trace formulae for Schrödinger operators with singular interactions / Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik -- An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ / Rafael D. Benguria, Soledad Benguria -- Twisted waveguide with a Neumann window / Philippe Briet, Hiba Hammedi -- Example of a periodic Neumann waveguide with a gap in its spectrum / Giuseppe Cardone, Andrii Khrabustovskyi -- Two-dimensional time-dependent point interactions / Raffaele Carlone, Michele Correggi, Rodolfo Figari -- On resonant spectral gaps in quantum graphs / Ngoc T. Do, Peter Kuchment, Beng Ong -- Adiabatic theorem for a class of stochastic differential equations on a Hilbert space / Martin Fraas -- Eigenvalues of Schrödinger operators with complex surface potentials / Rupert L. Frank -- A lower bound to the spectral threshold in curved quantum layers / Pedro Freitas, David Krejčiřík -- To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions / Yaroslav Granovskyi, Mark M. Malamud, Hagen Neidhardt, Andrea Posilicano -- Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator / André Hänel, Timo Weidl -- Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality / Bernard Helffer, Rola Kiwan -- A mathematical modeling of electron–phonon interaction for small wave numbers close to zero / Masao Hirokawa -- The modified unitary Trotter–Kato and Zeno product formulas revisited / Takashi Ichinose -- Spectral asymptotics induced by approaching and diverging planar circles / Sylwia Kondej -- Spectral estimates for the Heisenberg Laplacian on cylinders / Hynek Kovařík, Bartosch Ruszkowski, Timo Weidl -- Variational proof of the existence of eigenvalues for star graphs / Konstantin Pankrashkin -- On the boundedness and compactness of weighted Green operators of second-order elliptic operators / Yehuda Pinchover -- Abstract graph-like spaces and vector-valued metric graphs / Olaf Post -- A Cayley–Hamiltonian theorem for periodic finite band matrices / Barry Simon -- Path topology dependence of adiabatic time evolution / Atushi Tanaka, Taksu Cheon -- On quantum graph filters with flat passbands / Ondřej Turek -- Comments on the Chernoff $\sqrt n$-lemma / Valentin Zagrebnov.

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This volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrödinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley–Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory. Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields.