The second eigenvalue of the Robin Laplacian is shown to be maximal for ball among domains fixed volume, negative values parameter $\alpha$ in regime connecting first nontrivial Neumann and Steklov eigenvalues, even somewhat beyond regime. result close optimal, since not when sufficiently large negative, problem admits no maximiser positive.

We consider a diagonalization of Witten’s star product for a ghost system of arbitrary background charge and Grassmann parity. To this end we use a bosonized formulation of such systems and a spectral analysis of Neumann matrices. We further identify a continuous Moyal product structure for a combined ghosts+matter system. The normalization of multiplication kernel is discussed. ∗On leave from ...

We study the existence of nontrivial solutions for the problem ∆u = u, in a bounded smooth domain Ω ⊂ RN, with a semilinear boundary condition given by ∂u/∂ν = λu− W(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ∈ ]0,λ1]; λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variatio...

Different generators of a deformed oscillator algebra give rise to oneparameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the q-coherent states and with ’coordinate’ operators Jacobi matrices, are also pointed out. Permanent add...

E.O. Kiktenko, 2 N.O. Pozhar, M.N. Anufriev, A.S. Trushechkin, 2 R.R. Yunusov, Y.V. Kurochkin, A.I. Lvovsky, 3 and A.K. Fedorov 4 Russian Quantum Center, Skolkovo, Moscow 143025, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia Institute for Quantum Science and Technology, University of Calgary, Calgary AB T2N 1N4, Canada LPTMS, CNRS, Univ. Paris-Sud, ...

A.S. Trushechkin, 2, 3 E.O. Kiktenko, 4 and A.K. Fedorov 5, 6 Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia National Research Nuclear University MEPhI, Moscow 115409, Russia Department of Mathematics and Russian Quantum Center, National University of Science and Technology MISiS, Moscow 119049, Russia Bauman Moscow State Technical University, Moscow 105005...

A.S. Trushechkin, 2, 3 P.A. Tregubov, E.O. Kiktenko, 4 Y.V. Kurochkin, 3 and A.K. Fedorov 3, 5 Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia National Research Nuclear University “MEPhI”, Moscow 115409, Russia Department of Mathematics and Russian Quantum Center, National University of Science and Technology MISiS, Moscow 119049, Russia Russian Quantum Cent...