Related papers: Wave function for $GL(n,\mathbb{R})$ hyperbolic Su…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
We lift any (infinitesimal) unitary irreducible representation of $GL_n(\mathbb{R})$ to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of $\mathbb{R}^n\rtimes…
In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles.
We study the geodesic flow on the unit cotangent bundle $M=S^{*}\mathcal{N}$ of a closed hyperbolic surface $\mathcal{N}$, using the representation theory of $SL_{2}(\mathbb{R})$. We construct explicit $X$-adapted Hilbert spaces, obtained…
We present a derivation using kinetic wave theory of the two-dimensional empirical Garrett--Munk spectrum for ocean internal waves, valid at all frequencies including near-inertial frequencies. This is based directly on the governing…
We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperbolic-parabolic system is known to allow viscous shocks…
In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward…
Using a recursive formula for the Mellin transform $T_{n,a}(s)$ of a spherical, principal series $GL(n,\mathbb{R})$ Whittaker function, we develop an explicit recurrence relation for this Mellin transform. This relation, for any $n\ge2$,…
We study the so-called averaging functors from the geometric Langlands program in the setting of Fargues' program. This makes explicit certain cases of the spectral action which was recently introduced by Fargues-Scholze in the local…
Nonperturbative determinations of the renormalization group $\beta$ function are essential to connect lattice results to perturbative predictions of strongly coupled gauge theories and to determine the $\Lambda$ parameter or the strong…
We develop a theory of the quasi-static electrodynamic Green's function of deep subwavelength optical cavities containing an hyperbolic medium. We apply our theory to one-dimensional cavities realized using an hexagonal boron nitride and a…
We derive from first principles third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN-accurate dynamics of non-spinning compact binaries in hyperbolic orbits. Orbital elements and functions of the parametric…
A classical theorem of Mihlin yields Lp estimates for spectral multipliers Lp(R^d) -> Lp(R^d); g -> F^{-1}[f(| |^2) Fg] in terms of L^\infty bounds of the multiplier function f and its weighted derivatives up to an order > d/2. This…
On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes…
This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haar sequence has been used by Pettersson, Iaccarino,…
We introduce a coarse flow space for relatively hyperbolic groups and use it to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell-Jones Conjecture for relatively…
The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.
Construction and classification of 2D superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of…
We introduce a new approach to the study of modulation of high-frequency periodic wave patterns, based on pseudodifferential analysis, multi-scale expansion, and Kreiss symmetrizer estimates like those in hyperbolic and hyperbolic-parabolic…