no code implementations • 5 Jan 2021 • Marcel Filoche, Svitlana Mayboroda, Terence Tao
In the presence of a confining potential $V$, the eigenfunctions of a continuous Schr\"odinger operator $-\Delta +V$ decay exponentially with the rate governed by the part of $V$ which is above the corresponding eigenvalue; this can be quantified by a method of Agmon.
Mathematical Physics Mathematical Physics
no code implementations • 4 Dec 2020 • Laura Cladek, Terence Tao
We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions of these sets.
Classical Analysis and ODEs 11B30, 28A80
no code implementations • 1 Oct 2020 • Asgar Jamneshan, Terence Tao
We collect several foundational results regarding the interaction between locally compact spaces, probability spaces and probability algebras, and commutative $C^*$-algebras and von Neumann algebras equipped with traces, in the "uncountable" setting in which no separability, metrizability, or standard Borel hypotheses are placed on these spaces and algebras.
Functional Analysis Category Theory Operator Algebras Probability 28A60, 46L05, 28A50
5 code implementations • 10 Aug 2019 • Peter B. Denton, Stephen J. Parke, Terence Tao, Xining Zhang
We also provide a number of proofs and generalizations of the identity.
Rings and Algebras High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Mathematical Physics 15A18 (Primary) 15A42, 15B57 (Secondary)
no code implementations • 13 Feb 2007 • Terence Tao
Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously.
History and Overview 00A30
