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## Zhou, Xiaowen

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 Author ID: zhou.xiaowen Published as: Zhou, X.; Zhou, X. W.; Zhou, X.-W.; Zhou, Xiao Wen; Zhou, Xiao-Wen; Zhou, Xiaowen Homepage: https://www.concordia.ca/faculty/xiaowen-zhou.html External Links: MGP · ResearchGate · dblp
 Documents Indexed: 66 Publications since 1991, including 2 Books
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#### Co-Authors

 10 single-authored 6 Li, Yingqiu 6 Li, Zenghu 5 Renaud, Jean-François 5 Zhou, Jianwei 4 Xiong, Jie 3 Albrecher, Hansjörg 3 Li, Bo 3 Liu, Huili 3 Yang, Xu 2 Avram, Florin 2 Chen, Ye 2 Evans, Steven Neil 2 He, Hui 2 Landriault, David 2 Li, Bin 2 Li, Peisen 2 Vu, Nhat Linh 2 Wang, Wenyuan 2 Zhu, Na 1 Dawson, Donald Andrew 1 Dong, Hua 1 Donnelly, Peter 1 Evans, T. Matthew 1 Feng, Shui 1 Fleischmann, Klaus 1 Foucart, Clément 1 Hickey, Donal A. 1 Ivanovs, Jevgeņijs 1 Jiang, Yiming 1 Kermany, Amir R. R. 1 Kortschak, Dominik 1 Kurtz, Thomas Gordon 1 Kyprianou, Andreas E. 1 Loeffen, Ronnie L. 1 Schmuland, Byron 1 Tang, Qihe 1 Vaillancourt, Jean 1 Wang, Hao 1 Wang, Li 1 Wang, Suxin 1 Wei, Tingting 1 Yang, Xiangqun 1 Yin, Chuancun 1 Zhao, Shiwei
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#### Serials

 9 Journal of Applied Probability 5 Statistics & Probability Letters 5 Stochastic Processes and their Applications 3 Journal of Theoretical Probability 3 Electronic Journal of Probability 3 Electronic Communications in Probability 3 Frontiers of Mathematics in China 2 Canadian Journal of Mathematics 2 Journal of Differential Equations 2 Insurance Mathematics & Economics 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Advances in Applied Probability 1 Journal of Mathematical Analysis and Applications 1 The Annals of Probability 1 Canadian Mathematical Bulletin 1 Theoretical Population Biology 1 Journal of Engineering Mathematics (Xi’an) 1 Chinese Journal of Applied Probability and Statistics 1 Probability Theory and Related Fields 1 The Annals of Applied Probability 1 Chinese Science Bulletin 1 Potential Analysis 1 Theory of Probability and Mathematical Statistics 1 Applied Mathematical Finance 1 Bernoulli 1 Acta Mathematica Sinica. English Series 1 Methodology and Computing in Applied Probability 1 International Journal of Pure and Applied Mathematics 1 North American Actuarial Journal 1 Communications on Stochastic Analysis
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#### Fields

 58 Probability theory and stochastic processes (60-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Biology and other natural sciences (92-XX) 1 Partial differential equations (35-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

45 Publications have been cited 539 times in 266 Documents Cited by Year
Occupation times of intervals until first passage times for spectrally negative Lévy processes. Zbl 1287.60062
Loeffen, Ronnie L.; Renaud, Jean-François; Zhou, Xiaowen
2014
Occupation times of spectrally negative Lévy processes with applications. Zbl 1227.60061
Landriault, David; Renaud, Jean-François; Zhou, Xiaowen
2011
An insurance risk model with Parisian implementation delays. Zbl 1319.60098
Landriault, David; Renaud, Jean-François; Zhou, Xiaowen
2014
Exit identities for Lévy processes observed at Poisson arrival times. Zbl 1338.60125
Albrecher, Hansjörg; Ivanovs, Jevgenijs; Zhou, Xiaowen
2016
A Lévy insurance risk process with tax. Zbl 1144.60032
Albrecher, Hansjörg; Renaud, Jean-François; Zhou, Xiaowen
2008
General tax structures and the Lévy insurance risk model. Zbl 1210.60098
Kyprianou, Andreas E.; Zhou, Xiaowen
2009
Distribution of the present value of dividend payments in a Lévy risk model. Zbl 1132.60041
Renaud, Jean-François; Zhou, Xiaowen
2007
On a classical risk model with a constant dividend barrier. Zbl 1215.60051
Zhou, Xiaowen
2005
The joint Laplace transforms for diffusion occupation times. Zbl 1370.60136
Li, Bin; Zhou, Xiaowen
2013
Stochastic generalized Burgers equations driven by fractional noises. Zbl 1250.60027
Jiang, Yiming; Wei, Tingting; Zhou, Xiaowen
2012
On pre-exit joint occupation times for spectrally negative Lévy processes. Zbl 1315.60049
Li, Yingqiu; Zhou, Xiaowen
2014
Exit problems for spectrally negative Lévy processes reflected at either the supremum or the infimum. Zbl 1132.60042
Zhou, Xiaowen
2007
Pricing of Parisian options for a jump-diffusion model with two-sided jumps. Zbl 1372.91100
Albrecher, Hansjörg; Kortschak, Dominik; Zhou, Xiaowen
2012
Two-sided discounted potential measures for spectrally negative Lévy processes. Zbl 1320.60113
Li, Yingqiu; Zhou, Xiaowen; Zhu, Na
2015
On the last exit times for spectrally negative Lévy processes. Zbl 1400.60068
Li, Yingqiu; Yin, Chuancun; Zhou, Xiaowen
2017
On taxed spectrally negative Lévy processes with draw-down stopping. Zbl 1395.91245
Avram, Florin; Vu, Nhat Linh; Zhou, Xiaowen
2017
A time-homogeneous diffusion model with tax. Zbl 1271.62246
Li, Bin; Tang, Qihe; Zhou, Xiaowen
2013
Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees. Zbl 1023.60082
Donnelly, Peter; Evans, Steven N.; Fleischmann, Klaus; Kurtz, Thomas G.; Zhou, Xiaowen
2000
When does surplus reach a certain level before ruin? Zbl 1117.91387
Zhou, Xiaowen
2004
Diffusion occupation time before exiting. Zbl 1308.60093
Li, Yingqiu; Wang, Suxin; Zhou, Xiaowen; Zhu, Na
2014
General drawdown-based de Finetti optimization for spectrally negative Lévy risk processes. Zbl 1396.91314
Wang, Wenyuan; Zhou, Xiaowen
2018
A general continuous-state nonlinear branching process. Zbl 07120715
Li, Pei-Sen; Yang, Xu; Zhou, Xiaowen
2019
Exit problems for general draw-down times of spectrally negative Lévy processes. Zbl 1415.60048
Li, Bo; Vu, Nhat Linh; Zhou, Xiaowen
2019
Joint stationary moments of a two-island diffusion model of population subdivision. Zbl 1210.92017
Kermany, Amir R. R.; Zhou, Xiaowen; Hickey, Donal A.
2008
Superprocesses with coalescing Brownian spatial motion as large-scale limits. Zbl 1067.60085
Dawson, D. A.; Li, Z.; Zhou, X.
2004
On the robustness of the damped $$V$$-cycle of the wavelet frequency decomposition multigrid method. Zbl 0809.65118
Rieder, A.; Zhou, X.
1994
On fluctuation theory for spectrally negative Lévy processes with Parisian reflection below, and applications. Zbl 1382.60071
Avram, Florin; Zhou, Xiaowen
2017
A joint Laplace transform for pre-exit diffusion of occupation times. Zbl 1370.60134
Chen, Ye; Yang, Xiang Qun; Li, Ying Qiu; Zhou, Xiao Wen
2017
Pathwise uniqueness for an SPDE with Hölder continuous coefficient driven by $$\alpha$$-stable noise. Zbl 1357.60067
Yang, Xu; Zhou, Xiaowen
2017
The reversibility and an SPDE for the generalized Fleming-Viot processes with mutation. Zbl 1291.60104
Li, Zenghu; Liu, Huili; Xiong, Jie; Zhou, Xiaowen
2013
The compact support property for the $$\Lambda$$-Fleming-Viot process with underlying Brownian motion. Zbl 1260.60098
Liu, Huili; Zhou, Xiaowen
2012
Superprocess over a stochastic flow with superprocess catalyst. Zbl 1063.60123
Xiong, Jie; Zhou, Xiaowen
2004
On weighted occupation times for refracted spectrally negative Lévy processes. Zbl 1404.60066
Li, Bo; Zhou, Xiaowen
2018
An occupation time related potential measure for diffusion processes. Zbl 1370.60133
Chen, Ye; Li, Yingqiu; Zhou, Xiaowen
2017
A coupled finite difference material point method and its application in explosion simulation. Zbl 1356.80062
Cui, X. X.; Zhang, X.; Zhou, X.; Liu, Y.; Zhang, F.
2014
A zero-one law of almost sure local extinction for $$(1+\beta)$$-super-Brownian motion. Zbl 1151.60332
Zhou, Xiaowen
2008
Stepping-stone model with circular Brownian migration. Zbl 1145.92026
Zhou, Xiaowen
2008
A superprocess involving both branching and coalescing. Zbl 1126.60086
Zhou, Xiaowen
2007
On the duality between coalescing Brownian motions. Zbl 1063.60118
Xiong, Jie; Zhou, Xiaowen
2005
Clustering behavior of a continuous-sites stepping-stone model with Brownian migration. Zbl 1064.60074
Zhou, Xiaowen
2003
On a spectrally negative Lévy risk process with periodic dividends and capital injections. Zbl 1425.91221
Dong, Hua; Zhou, Xiaowen
2019
A distribution-function-valued SPDE and its applications. Zbl 1358.60074
Wang, Li; Yang, Xu; Zhou, Xiaowen
2017
Reversibility of interacting Fleming-Viot processes with mutation, selection, and recombination. Zbl 1229.92065
Feng, Shui; Schmuland, Byron; Vaillancourt, Jean; Zhou, Xiaowen
2011
Some fluctuation identities for Lévy processes with jumps of the same sign. Zbl 1064.60102
Zhou, Xiaowen
2004
Sample function properties of two-parameter Markov processes. Zbl 0788.60063
Zhou, Xiao-Wen; Zhou, Jian-Wei
1993
A general continuous-state nonlinear branching process. Zbl 07120715
Li, Pei-Sen; Yang, Xu; Zhou, Xiaowen
2019
Exit problems for general draw-down times of spectrally negative Lévy processes. Zbl 1415.60048
Li, Bo; Vu, Nhat Linh; Zhou, Xiaowen
2019
On a spectrally negative Lévy risk process with periodic dividends and capital injections. Zbl 1425.91221
Dong, Hua; Zhou, Xiaowen
2019
General drawdown-based de Finetti optimization for spectrally negative Lévy risk processes. Zbl 1396.91314
Wang, Wenyuan; Zhou, Xiaowen
2018
On weighted occupation times for refracted spectrally negative Lévy processes. Zbl 1404.60066
Li, Bo; Zhou, Xiaowen
2018
On the last exit times for spectrally negative Lévy processes. Zbl 1400.60068
Li, Yingqiu; Yin, Chuancun; Zhou, Xiaowen
2017
On taxed spectrally negative Lévy processes with draw-down stopping. Zbl 1395.91245
Avram, Florin; Vu, Nhat Linh; Zhou, Xiaowen
2017
On fluctuation theory for spectrally negative Lévy processes with Parisian reflection below, and applications. Zbl 1382.60071
Avram, Florin; Zhou, Xiaowen
2017
A joint Laplace transform for pre-exit diffusion of occupation times. Zbl 1370.60134
Chen, Ye; Yang, Xiang Qun; Li, Ying Qiu; Zhou, Xiao Wen
2017
Pathwise uniqueness for an SPDE with Hölder continuous coefficient driven by $$\alpha$$-stable noise. Zbl 1357.60067
Yang, Xu; Zhou, Xiaowen
2017
An occupation time related potential measure for diffusion processes. Zbl 1370.60133
Chen, Ye; Li, Yingqiu; Zhou, Xiaowen
2017
A distribution-function-valued SPDE and its applications. Zbl 1358.60074
Wang, Li; Yang, Xu; Zhou, Xiaowen
2017
Exit identities for Lévy processes observed at Poisson arrival times. Zbl 1338.60125
Albrecher, Hansjörg; Ivanovs, Jevgenijs; Zhou, Xiaowen
2016
Two-sided discounted potential measures for spectrally negative Lévy processes. Zbl 1320.60113
Li, Yingqiu; Zhou, Xiaowen; Zhu, Na
2015
Occupation times of intervals until first passage times for spectrally negative Lévy processes. Zbl 1287.60062
Loeffen, Ronnie L.; Renaud, Jean-François; Zhou, Xiaowen
2014
An insurance risk model with Parisian implementation delays. Zbl 1319.60098
Landriault, David; Renaud, Jean-François; Zhou, Xiaowen
2014
On pre-exit joint occupation times for spectrally negative Lévy processes. Zbl 1315.60049
Li, Yingqiu; Zhou, Xiaowen
2014
Diffusion occupation time before exiting. Zbl 1308.60093
Li, Yingqiu; Wang, Suxin; Zhou, Xiaowen; Zhu, Na
2014
A coupled finite difference material point method and its application in explosion simulation. Zbl 1356.80062
Cui, X. X.; Zhang, X.; Zhou, X.; Liu, Y.; Zhang, F.
2014
The joint Laplace transforms for diffusion occupation times. Zbl 1370.60136
Li, Bin; Zhou, Xiaowen
2013
A time-homogeneous diffusion model with tax. Zbl 1271.62246
Li, Bin; Tang, Qihe; Zhou, Xiaowen
2013
The reversibility and an SPDE for the generalized Fleming-Viot processes with mutation. Zbl 1291.60104
Li, Zenghu; Liu, Huili; Xiong, Jie; Zhou, Xiaowen
2013
Stochastic generalized Burgers equations driven by fractional noises. Zbl 1250.60027
Jiang, Yiming; Wei, Tingting; Zhou, Xiaowen
2012
Pricing of Parisian options for a jump-diffusion model with two-sided jumps. Zbl 1372.91100
Albrecher, Hansjörg; Kortschak, Dominik; Zhou, Xiaowen
2012
The compact support property for the $$\Lambda$$-Fleming-Viot process with underlying Brownian motion. Zbl 1260.60098
Liu, Huili; Zhou, Xiaowen
2012
Occupation times of spectrally negative Lévy processes with applications. Zbl 1227.60061
Landriault, David; Renaud, Jean-François; Zhou, Xiaowen
2011
Reversibility of interacting Fleming-Viot processes with mutation, selection, and recombination. Zbl 1229.92065
Feng, Shui; Schmuland, Byron; Vaillancourt, Jean; Zhou, Xiaowen
2011
General tax structures and the Lévy insurance risk model. Zbl 1210.60098
Kyprianou, Andreas E.; Zhou, Xiaowen
2009
A Lévy insurance risk process with tax. Zbl 1144.60032
Albrecher, Hansjörg; Renaud, Jean-François; Zhou, Xiaowen
2008
Joint stationary moments of a two-island diffusion model of population subdivision. Zbl 1210.92017
Kermany, Amir R. R.; Zhou, Xiaowen; Hickey, Donal A.
2008
A zero-one law of almost sure local extinction for $$(1+\beta)$$-super-Brownian motion. Zbl 1151.60332
Zhou, Xiaowen
2008
Stepping-stone model with circular Brownian migration. Zbl 1145.92026
Zhou, Xiaowen
2008
Distribution of the present value of dividend payments in a Lévy risk model. Zbl 1132.60041
Renaud, Jean-François; Zhou, Xiaowen
2007
Exit problems for spectrally negative Lévy processes reflected at either the supremum or the infimum. Zbl 1132.60042
Zhou, Xiaowen
2007
A superprocess involving both branching and coalescing. Zbl 1126.60086
Zhou, Xiaowen
2007
On a classical risk model with a constant dividend barrier. Zbl 1215.60051
Zhou, Xiaowen
2005
On the duality between coalescing Brownian motions. Zbl 1063.60118
Xiong, Jie; Zhou, Xiaowen
2005
When does surplus reach a certain level before ruin? Zbl 1117.91387
Zhou, Xiaowen
2004
Superprocesses with coalescing Brownian spatial motion as large-scale limits. Zbl 1067.60085
Dawson, D. A.; Li, Z.; Zhou, X.
2004
Superprocess over a stochastic flow with superprocess catalyst. Zbl 1063.60123
Xiong, Jie; Zhou, Xiaowen
2004
Some fluctuation identities for Lévy processes with jumps of the same sign. Zbl 1064.60102
Zhou, Xiaowen
2004
Clustering behavior of a continuous-sites stepping-stone model with Brownian migration. Zbl 1064.60074
Zhou, Xiaowen
2003
Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees. Zbl 1023.60082
Donnelly, Peter; Evans, Steven N.; Fleischmann, Klaus; Kurtz, Thomas G.; Zhou, Xiaowen
2000
On the robustness of the damped $$V$$-cycle of the wavelet frequency decomposition multigrid method. Zbl 0809.65118
Rieder, A.; Zhou, X.
1994
Sample function properties of two-parameter Markov processes. Zbl 0788.60063
Zhou, Xiao-Wen; Zhou, Jian-Wei
1993
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#### Cited by 319 Authors

 29 Zhou, Xiaowen 16 Palmowski, Zbigniew 13 Wang, Wenyuan 12 Landriault, David 12 Renaud, Jean-François 11 Czarna, Irmina 11 Pérez Garmendia, Jose Luis 10 Cheung, Eric C. K. 10 Li, Bin 10 Yamazaki, Kazutoshi 8 Avram, Florin 8 Loeffen, Ronnie L. 8 Yin, Chuancun 7 Albrecher, Hansjörg 7 Kyprianou, Andreas E. 7 Li, Yingqiu 7 Xiong, Jie 7 Yan, Litan 6 Dong, Hua 6 Hu, Yijun 6 Li, Zenghu 6 Liu, Junfeng 6 Zhang, Zhimin 5 Frostig, Esther 5 Li, Bo 5 Ming, Ruixing 5 Yang, Hailiang 5 Yuen, Kam Chuen 4 Cui, Zhenyu 4 Feng, Runhuan 4 Ivanovs, Jevgeņijs 4 Ko, Jeonghwan 4 Kurdila, Andrew J. 4 Lkabous, Mohamed Amine 4 Wang, Yongjin 4 Wong, Jeff T. Y. 4 Wu, Lan 4 Xia, Dengfeng 4 Yang, Xu 4 Zhang, Hongzhong 3 Blath, Jochen 3 Casanova, Adrián González 3 Chen, Mi 3 Chen, Ping 3 Chen, Ye 3 He, Hui 3 Jiang, Yiming 3 Jiang, Zhou 3 Li, Peisen 3 Li, Shuanming 3 Li, Yanhong 3 Pardo, Juan Carlos 3 Song, Renming 3 Surya, Budhi Arta 3 Wang, Suxin 3 Wilke-Berenguer, Maite 3 Willmot, Gordon E. 3 Wu, Xueyuan 3 Yang, Xiaoyuan 3 Zhang, Chunsheng 3 Zhang, Yinghan 3 Zhao, Chunming 3 Zhao, Xianghua 2 Bekker, René 2 Biffis, Enrico 2 Bo, Lijun 2 Buzzoni, Eugenio 2 Dai, Hongshuai 2 Dębicki, Krzysztof 2 Gao, Heli 2 Griffin, Philip S. 2 Guérin, Hélène 2 Guo, Junyi 2 Hammer, Matthias 2 Huang, Yujuan 2 Keren-Pinhasik, Adva 2 Lars Kirkby, J. 2 Li, Danping 2 Li, Dongchen 2 Li, Shu 2 Li, Zhong 2 Lian, Yanping 2 Liu, Haibo 2 Liu, Huili 2 Liu, Zaiming 2 Mandjes, Michel Robertus Hendrikus 2 Morales, Manuel 2 Nguyen, Duy-Minh 2 Noba, Kei 2 Ortgiese, Marcel 2 Peng, Xingchun 2 Peralta, Oscar 2 Pilant, Michael S. 2 Shi, Tianxiang 2 Shimizu, Yasutaka 2 Starreveld, Nicos J. 2 Sun, Xichao 2 Tang, Qihe 2 Völlering, Florian 2 Vu, Nhat Linh ...and 219 more Authors
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#### Cited in 78 Serials

 39 Insurance Mathematics & Economics 21 Journal of Applied Probability 19 Statistics & Probability Letters 15 Stochastic Processes and their Applications 13 Scandinavian Actuarial Journal 9 Journal of Computational and Applied Mathematics 9 Journal of Theoretical Probability 7 Methodology and Computing in Applied Probability 6 Applied Mathematics and Computation 6 Frontiers of Mathematics in China 5 Advances in Applied Probability 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Applied Mathematics. Series B (English Edition) 4 Journal of Mathematical Analysis and Applications 4 The Annals of Applied Probability 4 Electronic Journal of Probability 4 Stochastics and Dynamics 3 The Annals of Probability 3 Applied Mathematics and Optimization 3 Journal of Optimization Theory and Applications 3 Probability Theory and Related Fields 3 Mathematical Problems in Engineering 3 ASTIN Bulletin 3 Journal of Industrial and Management Optimization 3 European Actuarial Journal 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Biology 2 Stochastic Analysis and Applications 2 Computational Mechanics 2 Potential Analysis 2 Bernoulli 2 Finance and Stochastics 2 Discrete Dynamics in Nature and Society 2 Stochastic Models 2 Advances in Difference Equations 2 Stochastics 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Computational Physics 1 Lithuanian Mathematical Journal 1 Physica A 1 Mathematics of Operations Research 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Operations Research Letters 1 Probability and Mathematical Statistics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Queueing Systems 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Communications in Numerical Methods in Engineering 1 Theory of Probability and Mathematical Statistics 1 Journal of Mathematical Sciences (New York) 1 Random Operators and Stochastic Equations 1 NoDEA. Nonlinear Differential Equations and Applications 1 Applied Mathematical Finance 1 Electronic Communications in Probability 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Abstract and Applied Analysis 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Fractional Calculus & Applied Analysis 1 International Journal of Theoretical and Applied Finance 1 Acta Mathematica Sinica. English Series 1 Quantitative Finance 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 North American Actuarial Journal 1 Boundary Value Problems 1 Journal of the Korean Statistical Society 1 Blätter der DGVFM (Deutsche Gesellschaft für Versicherungs- und Finanzmathematik) 1 SIAM Journal on Financial Mathematics 1 Science China. Mathematics 1 Journal of Applied Analysis and Computation 1 Stochastic Systems 1 Modern Stochastics. Theory and Applications 1 Cogent Mathematics
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#### Cited in 23 Fields

 223 Probability theory and stochastic processes (60-XX) 150 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 30 Systems theory; control (93-XX) 25 Statistics (62-XX) 11 Partial differential equations (35-XX) 9 Numerical analysis (65-XX) 8 Operations research, mathematical programming (90-XX) 8 Biology and other natural sciences (92-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Integral transforms, operational calculus (44-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX)