Related papers: On the Whittaker Plancherel Theorem for Real Reduc…

We define extension $\infty$-categories for exact $\infty$-categories in terms of bifibrations. Extension $\infty$-categories are invariant when passing to the stable hull, and consequently we show that they form an $\Omega$-spectrum,…

This paper contains a non-trivial generalization of the Harish-Chandra transforms on a connected semisimple Lie group $G,$ with finite center, into what we term spherical convolutions. Among other results we show that its integral over the…

We present a proof of the generalized Kramers-Pasternack relation using the hyper-radial equation approach. Following Kramers' method, we manipulate the radial equation by multiplying it with an expression closely related to terms in the…

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in…

In this paper we continue the study of the notion of $\mathscr{P}$-rectifiability in Carnot groups. We say that a Radon measure is $\mathscr{P}_h$-rectifiable, for $h\in\mathbb N$, if it has positive $h$-lower density and finite $h$-upper…

In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James' Conjecture for Iwahori--Hecke algebras of exceptional type. The new…

We prove a Desch-Schappacher type perturbation theorem for one-parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework…

This is the second paper in a series of two in which a global algebraic number theory of the reals is formulated with the purpose of providing a unified setting for algebraic and transcendental number theory. In this paper, to any real…

This is the first paper in a series of two which proves a version of a theorem of Harish-Chandra for quantum symmetric spaces in the maximally split case: There is a Harish-Chandra map which induces an isomorphism between the ring of…

Let $G$ be a complex reductive group, $\theta \colon G \to G$ an involution, and $K = G^\theta$. In arXiv:1206.5547, W. Schmid and the second named author proposed a program to study unitary representations of the corresponding real form…

The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…

This paper has two main purposes. Firstly we generalise Ram's explicit construction of calibrated representations of the affine Hecke algebra to the multi-parameter case (including the non-reduced $BC_n$ case). We then derive the Plancherel…

It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf--Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018) is a special case of a more general statement, which can be…

The group theoretical approach to the relativistic wave equations on the real reducible spaces for spin~0, 1/2 and~1 massless particles is considered. The invariant wave equations which determine the appropriate irreducible representations…

We present a new interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincar\'e group. We argue that the…

Symmetry analysis can provide a suitable change of variables, i.e., in geometric terms, a suitable diffeomorphism that simplifies the given direction field, which can help significantly in solving or studying differential equations. Roughly…

We show that Arthur's Paley-Wiener theorem for K-finite compactly supported smooth functions on a real reductive Lie group G of the Harish-Chandra class can be deduced from the Paley-Wiener theorem we established in the more general setting…

There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the kernel of this map are convex cocompact in…

In a recent paper by M. Mantoiu and M. Ruzhansky, a global pseudo-differential calculus has been developed for unimodular groups of type I. In the present article we generalize the main results to arbitrary locally compact groups of type I.…

This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a…