PERFORM Publications

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Title		Authors	PubMed ID
1	Auditory Training for Everyday Functioning in Later Life	Li KZH; Campos J; Pichora-Fuller MK;	41036263 PSYCHOLOGY
2	Functions of Informal Subgroups in Relation to Work Groups and Group Effectiveness	Sidorenkov AV; Borokhovski EF;	40459704 CONCORDIA
3	Correlations of pilot trainees brainwave dynamics with subjective performance evaluations: insights from EEG microstate analysis	Zhao M; Law A; Su C; Jennings S; Bourgon A; Jia W; Larose MH; Bowness D; Zeng Y;	40109507 ENCS
4	Attention, working memory, and inhibitory control in aging: Comparing amateur singers, instrumentalists, and active controls	Joyal M; Sicard A; Penhune V; Jackson PL; Tremblay P;	39367878 PSYCHOLOGY
5	Comparative Analysis of the Functions Work Groups and Informal Subgroups Carry out in Relation to their Members: The Essence, Conditions of Implementation, Effects, and Dysfunctions	Sidorenkov AV; Borokhovski EF;	38492193 CONCORDIA
6	Childhood hyperactivity, eating behaviours, and executive functions: Their association with the development of eating-disorder symptoms in adolescence	Dufour R; Breton É; Morin AJS; Côté SM; Dubois L; Vitaro F; Boivin M; Tremblay RE; Booij L;	37833803 PSYCHOLOGY
7	Theory of mind development: State of the science and future directions.	Poulin-Dubois D	32859285 PSYCHOLOGY
8	Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach	Bertola M; Blackstone E; Katsevich A; Tovbis A;	32684912 MATHSTATS
9	Effects of Dance/Movement Training vs. Aerobic Exercise Training on cognition, physical fitness and quality of life in older adults: A randomized controlled trial.	Esmail A, Vrinceanu T, Lussier M, Predovan D, Berryman N, Houle J, Karelis A, Grenier S, Minh Vu TT, Villalpando JM, Bherer L	31987547 PERFORM

Title:	Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach
Authors:	Bertola M, Blackstone E, Katsevich A, Tovbis A
Link:	https://pubmed.ncbi.nlm.nih.gov/32684912/
DOI:	10.1007/s13324-020-00371-6
Publication:	Analysis and mathematical physics
Keywords:	Asymptotics of hypergeometric functions; Diagonalization of integral operators with continuous spectrum; Finite Hilbert transforms on multi intervals; Riemann-Hilbert problem; Spectral theory of finite Hilbert transforms;
PMID:	32684912	Category:	Anal Math Phys	Date Added:	2020-07-21
Dept Affiliation:	MATHSTATS 1 Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve W., Montréal, Québec H3G 1M8 Canada. 2 SISSA, International School for Advanced Studies, Via Bonomea 265, Trieste, Italy. 3 Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 114 28 Stockholm, Sweden. 4 Department of Mathematics, University of Central Florida, P.O. Box 161364, 4000 Central Florida Blvd, Orlando, FL 32816-1364 USA.

Description:

In this paper we study the spectra of bounded self-adjoint linear operators that are related to finite Hilbert transforms $H_{L} : L^{2} ([b_{L}, 0]) \to L^{2} ([0, b_{R}])$ and $H_{R} : L^{2} ([0, b_{R}]) \to L^{2} ([b_{L}, 0])$ . These operators arise when one studies the interior problem of tomography. The diagonalization of $H_{R}, H_{L}$ has been previously obtained, but only asymptotically when $b_{L} \neq - b_{R}$ . We implement a novel approach based on the method of matrix Riemann-Hilbert problems (RHP) which diagonalizes $H_{R}, H_{L}$ explicitly. We also find the asymptotics of the solution to a related RHP and obtain error estimates.

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