Related papers: Ode to commutator operators
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter…
This paper has been withdrawn by the author, due to a recent article by Kriete and Moorhouse (Linear relations in the Calkin algebra for composition operators, Trans. AMS, 359 (2007), 2915-2944) which includes more general results.
These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.
A brief remembrance of some aspects of the author's scientific interaction with Stephen Hawking. A contribution to Physics Today's March 14, 2018 web page in which Stephen Hawking is remembered by his colleagues.
This is an introduction of the volume of the journal Commentationes Mathematicae Universitatis Caroalinae dedicated to the memory of V\v{e}ra Trnkov\'a}.
This is a concise foreword to, rather than a review of D-brane physics.
In this paper, we make some remarks on Jos\'e Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
This note is the transcription of an interview with Professor Luigi Rodino, on the occasion of the ISAAC-ICMAM Conference of Analysis in Developing Countries (December 2, 2024 - Bogot\`a), that was dedicated to him. Luigi Rodino is at…
In this paper, we study the properties of closure operators obtained as initial lifts along a reflector, and compactness with respect to them in particular. Applications in the areas of topology, topological groups and topological…
Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.
I describe parts of my joint work with S. Deser [March 19, 1931 - April 21, 2023] which started when I was working as a post-doc at Brandeis University in 2001. Our work was mostly, but not exclusively, on conserved charges of higher…
Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{k\"obaLOC25}, where one is based on the coorbit theory of Feichtinger-Gr\"ochening while the other is…
Alex, the main discoverer of high Tc superconductivity, was also a dear friend. Here I offer a few frank anecdotes, possibly inaccurate in some details but heartfelt and accurate in the substance, as a personal tribute to our friendship.
This is a preliminary version of the textbook on integrable systems. The work has been partly supported by Grant Nr.10/2006-RU, Austrian Academic Exchange Service \"OAD and Grant P20164-N18, Austrian Science Fund FWF
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
This is the write-up of the talk I gave at the 23rd International Symposium on Mathematical Programming (ISMP) in Bordeaux, France, July 6th, 2018. The talk was a general overview of the state of the art of time-varying, mainly convex,…