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## Gómez-Ullate, David

Compute Distance To:
 Author ID: gomez-ullate.david Published as: Gómez-Ullate, D.; Gómez-Ullate, David; Gomez-Ullate, David; Gómez-Ullate, Daivd; Gomez-Ullate, D. External Links: MGP
 Documents Indexed: 45 Publications since 1999, including 1 Book
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#### Co-Authors

 0 single-authored 25 Milson, Robert 12 Kamran, Niky 8 González-López, Artemio 8 Grandati, Yves 6 Calogero, Francesco A. 6 Finkel, Federico 3 García-Ferrero, Maria Ángeles 3 Santini, Paolo Maria 3 Sommacal, Matteo 2 Gonzáles-López, A. 2 Winternitz, Pavel 1 Clarkson, Peter A. 1 Fedorov, Yuri N. 1 Iserles, Arieh 1 Kasman, Alex 1 Kuijlaars, Arno B. J. 1 Lafortune, Stéphane 1 Levi, Decio 1 Marcellán Español, Francisco 1 Mcintyre, Zoé 1 Olver, Peter John 1 Quispel, Reinout 1 Rodríiguez, M. A. 1 Tempesta, Piergiulio
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#### Serials

 6 Journal of Physics A: Mathematical and General 6 Journal of Physics A: Mathematical and Theoretical 4 Journal of Mathematical Analysis and Applications 3 Journal of Approximation Theory 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Studies in Applied Mathematics 2 Physica D 1 Inverse Problems 1 Letters in Mathematical Physics 1 Nuclear Physics. B 1 Physics Letters. B 1 Theoretical and Mathematical Physics 1 Advances in Mathematics 1 Discrete and Continuous Dynamical Systems 1 Journal of Nonlinear Mathematical Physics 1 Foundations of Computational Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 CRM Proceedings & Lecture Notes
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#### Fields

 24 Quantum theory (81-XX) 23 Ordinary differential equations (34-XX) 18 Special functions (33-XX) 10 Dynamical systems and ergodic theory (37-XX) 5 Partial differential equations (35-XX) 5 Operator theory (47-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Mechanics of particles and systems (70-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX)

#### Citations contained in zbMATH Open

39 Publications have been cited 581 times in 207 Documents Cited by Year
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem. Zbl 1183.34033
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2009
An extension of Bochner’s problem: exceptional invariant subspaces. Zbl 1214.34079
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2010
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. Zbl 1283.81059
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2014
Exceptional orthogonal polynomials and the Darboux transformation. Zbl 1202.81036
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2010
Two-step Darboux transformations and exceptional Laguerre polynomials. Zbl 1232.33013
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2012
A conjecture on exceptional orthogonal polynomials. Zbl 1282.33019
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2013
Recurrence relations for exceptional Hermite polynomials. Zbl 1336.33025
Gómez-Ullate, D.; Kasman, A.; Kuijlaars, A. B. J.; Milson, R.
2016
Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials. Zbl 1300.33013
Gómez-Ullate, David; Marcellán, Francisco; Milson, Robert
2013
On orthogonal polynomials spanning a non-standard flag. Zbl 1247.33016
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2012
The Darboux transformation and algebraic deformations of shape-invariant potentials. Zbl 1065.81126
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2004
Extended Krein-Adler theorem for the translationally shape invariant potentials. Zbl 1296.81023
Gomez-Ullate, David; Grandati, Yves; Milson, Robert
2014
A Bochner type characterization theorem for exceptional orthogonal polynomials. Zbl 1421.42014
García-Ferrero, M. Ángeles; Gómez-Ullate, David; Milson, Robert
2019
Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger’s equation. Zbl 1328.34030
García-Ferrero, Maria Ángeles; Gómez-Ullate, David
2015
Supersymmetry and algebraic Darboux transformations. Zbl 1064.81052
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2004
Asymptotically isochronous systems. Zbl 1161.70010
Calogero, Francesco; Gomez-Ullate, David
2008
The transition from regular to irregular motions, explained as travel on Riemann surfaces. Zbl 1157.70309
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
2005
Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials. Zbl 1408.33021
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2018
Quasi-exact solvability and the direct approach to invariant subspaces. Zbl 1088.81094
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2005
Exact solutions of a new elliptic Calogero-Sutherland model. Zbl 1062.81518
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2001
Dynamical systems on infinitely sheeted Riemann surfaces. Zbl 1130.37384
Fedorov, Yuri N.; Gómez-Ullate, David
2007
Quasi-exact solvability in a general polynomial setting. Zbl 1129.34056
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2007
Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials. Zbl 1400.33017
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2018
Symmetries of discrete dynamical systems involving two species. Zbl 0977.37035
Gómez-Ullate, D.; Lafortune, S.; Winternitz, P.
1999
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
$$A_N$$-type Dunkl operators and new spin Calogero-Sutherland models. Zbl 1025.81017
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2001
New spin Calogero-Sutherland models related to $$B_N$$-type Dunkl operators. Zbl 0972.81053
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2001
Structure theorems for linear and nonlinear differential operators admitting invariant polynomial subspaces. Zbl 1128.47043
Gómez-Ullate, Daivd; Kamran, Niky; Milson, Robert
2007
Understanding complex dynamics by means of an associated Riemann surface. Zbl 1280.37052
Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.; Calogero, F.
2012
Two novel classes of solvable many-body problems of goldfish type with constraints. Zbl 1126.70006
Calogero, F.; Gómez-Ullate, D.
2007
A new class of solvable many-body problems with constraints, associated with an exceptional polynomial subspace of codimension 2. Zbl 1147.82004
Calogero, F.; Gómez-Ullate, D.
2007
Towards a theory of chaos explained as travel on Riemann surfaces. Zbl 1153.37349
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
2009
Corrigendum on the proof of completeness for exceptional Hermite polynomials: “Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials”. Zbl 1441.81087
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
Exceptional Legendre polynomials and confluent Darboux Transformations. Zbl 1466.33006
García-Ferrero, María Ángeles; Gómez-Ullate, David; Milson, Robert
2021
Quasi-exactly solvable generalizations of Calogero-Sutherland models. Zbl 0993.81067
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2001
On the Sutherland spin model of $$B_N$$ type and its associated spin chain. Zbl 1013.82007
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2003
A survey of quasi-exactly solvable systems and spin Calogero-Sutherland models. Zbl 1330.81189
Finkel, F.; Gómez-Ullate, D.; Gonzáles-López, A.; Rodríiguez, M. A.; Zhdanov, R.
2004
New algebraic quantum many-body problems. Zbl 0962.81079
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2000
Exceptional orthogonal polynomials and rational solutions to Painlevé equations. Zbl 1443.33014
Gómez-Ullate, David; Milson, Robert
2020
Complete classification of rational solutions of $$A_{2n}$$-Painlevé systems. Zbl 07358507
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2021
Exceptional Legendre polynomials and confluent Darboux Transformations. Zbl 1466.33006
García-Ferrero, María Ángeles; Gómez-Ullate, David; Milson, Robert
2021
Complete classification of rational solutions of $$A_{2n}$$-Painlevé systems. Zbl 07358507
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2021
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
Corrigendum on the proof of completeness for exceptional Hermite polynomials: “Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials”. Zbl 1441.81087
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
Exceptional orthogonal polynomials and rational solutions to Painlevé equations. Zbl 1443.33014
Gómez-Ullate, David; Milson, Robert
2020
A Bochner type characterization theorem for exceptional orthogonal polynomials. Zbl 1421.42014
García-Ferrero, M. Ángeles; Gómez-Ullate, David; Milson, Robert
2019
Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials. Zbl 1408.33021
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2018
Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials. Zbl 1400.33017
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2018
Recurrence relations for exceptional Hermite polynomials. Zbl 1336.33025
Gómez-Ullate, D.; Kasman, A.; Kuijlaars, A. B. J.; Milson, R.
2016
Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger’s equation. Zbl 1328.34030
García-Ferrero, Maria Ángeles; Gómez-Ullate, David
2015
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. Zbl 1283.81059
Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2014
Extended Krein-Adler theorem for the translationally shape invariant potentials. Zbl 1296.81023
Gomez-Ullate, David; Grandati, Yves; Milson, Robert
2014
A conjecture on exceptional orthogonal polynomials. Zbl 1282.33019
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2013
Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials. Zbl 1300.33013
Gómez-Ullate, David; Marcellán, Francisco; Milson, Robert
2013
Two-step Darboux transformations and exceptional Laguerre polynomials. Zbl 1232.33013
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2012
On orthogonal polynomials spanning a non-standard flag. Zbl 1247.33016
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2012
Understanding complex dynamics by means of an associated Riemann surface. Zbl 1280.37052
Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.; Calogero, F.
2012
An extension of Bochner’s problem: exceptional invariant subspaces. Zbl 1214.34079
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2010
Exceptional orthogonal polynomials and the Darboux transformation. Zbl 1202.81036
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2010
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem. Zbl 1183.34033
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2009
Towards a theory of chaos explained as travel on Riemann surfaces. Zbl 1153.37349
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
2009
Asymptotically isochronous systems. Zbl 1161.70010
Calogero, Francesco; Gomez-Ullate, David
2008
Dynamical systems on infinitely sheeted Riemann surfaces. Zbl 1130.37384
Fedorov, Yuri N.; Gómez-Ullate, David
2007
Quasi-exact solvability in a general polynomial setting. Zbl 1129.34056
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2007
Structure theorems for linear and nonlinear differential operators admitting invariant polynomial subspaces. Zbl 1128.47043
Gómez-Ullate, Daivd; Kamran, Niky; Milson, Robert
2007
Two novel classes of solvable many-body problems of goldfish type with constraints. Zbl 1126.70006
Calogero, F.; Gómez-Ullate, D.
2007
A new class of solvable many-body problems with constraints, associated with an exceptional polynomial subspace of codimension 2. Zbl 1147.82004
Calogero, F.; Gómez-Ullate, D.
2007
The transition from regular to irregular motions, explained as travel on Riemann surfaces. Zbl 1157.70309
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
2005
Quasi-exact solvability and the direct approach to invariant subspaces. Zbl 1088.81094
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2005
The Darboux transformation and algebraic deformations of shape-invariant potentials. Zbl 1065.81126
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2004
Supersymmetry and algebraic Darboux transformations. Zbl 1064.81052
Gómez-Ullate, D.; Kamran, N.; Milson, R.
2004
A survey of quasi-exactly solvable systems and spin Calogero-Sutherland models. Zbl 1330.81189
Finkel, F.; Gómez-Ullate, D.; Gonzáles-López, A.; Rodríiguez, M. A.; Zhdanov, R.
2004
On the Sutherland spin model of $$B_N$$ type and its associated spin chain. Zbl 1013.82007
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2003
Exact solutions of a new elliptic Calogero-Sutherland model. Zbl 1062.81518
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2001
$$A_N$$-type Dunkl operators and new spin Calogero-Sutherland models. Zbl 1025.81017
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2001
New spin Calogero-Sutherland models related to $$B_N$$-type Dunkl operators. Zbl 0972.81053
Finkel, F.; Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.; Zhdanov, R.
2001
Quasi-exactly solvable generalizations of Calogero-Sutherland models. Zbl 0993.81067
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2001
New algebraic quantum many-body problems. Zbl 0962.81079
Gómez-Ullate, D.; González-López, A.; Rodríguez, M. A.
2000
Symmetries of discrete dynamical systems involving two species. Zbl 0977.37035
Gómez-Ullate, D.; Lafortune, S.; Winternitz, P.
1999
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#### Cited by 183 Authors

 18 Calogero, Francesco A. 17 Gómez-Ullate, David 16 Duran, Antonio J. 16 Milson, Robert 14 Quesne, Christiane 13 Odake, Satoru 12 Schulze-Halberg, Axel 11 Grandati, Yves 11 Sasaki, Ryu 9 Marquette, Ian 6 Bihun, Oksana 5 Bonneux, Niels 5 Roy, Pinaki 5 Winternitz, Pavel 4 Kamran, Niky 4 Langmann, Edwin 4 Roy, Barnana 3 García-Ferrero, Maria Ángeles 3 Hallnäs, Martin A. 3 Ho, Choon-Lin 3 Hoffmann, Scott E. 3 Horváth, Ágota P. 3 Hussin, Véronique 3 Leyvraz, Francois 3 Liaw, Constanze 3 Mandal, Bhabani Prasad 3 Stevens, Marco 3 Takemura, Kouichi 3 Turbiner, Alexander 3 Veselov, Alexander Petrovich 3 Zhang, Yaozhong 2 Bagchi, Bijan Kumar 2 Basu-Mallick, Bireswar 2 Bruschi, Mario 2 Crampé, Nicolas 2 Dorodnitsyn, Vladimir A. 2 Enolskiĭ, Viktor Zelikovich 2 Fernández C., David J. 2 Finkel, Federico 2 González-López, Artemio 2 Grosu, Codruţ 2 Grosu, Corina 2 Gurkan, Zeynep Nilhan 2 Hartmann, Betti 2 Kagramanova, Valeria 2 Kasman, Alex 2 Kelly Stewart, Jessica 2 Khare, Avinash 2 Kozlov, Roman 2 Kuijlaars, Arno B. J. 2 Kumari, Nisha 2 Kunz, Jutta 2 Lämmerzahl, Claus 2 Littlejohn, Lance L. 2 Miller, Willard jun. 2 Moreno-Balcázar, Juan José 2 Pashaev, Oktay K. 2 Pérez, Mario 2 Saad, Nasser 2 Santini, Paolo Maria 2 Shen, Shoufeng 2 Tanaka, Toshiaki 2 Tsujimoto, Satoshi 2 Yadav, Rajesh Kumar 2 Yeşiltaş, Özlem 1 Abedzadeh, A. 1 Alici, Haydar 1 Area, Iván 1 Arsenault, Ashley 1 Atia, Mohamed Jalel 1 Baradaran, Marzieh 1 Bassom, Andrew P. 1 Bender, Carl M. 1 Bérard, Alain 1 Bermúdez, David 1 Boreskov, Konstantin G. 1 Bracciali, Cleonice F. 1 Brihaye, Yves 1 Cariñena, José F. 1 Celeghini, Enrico 1 Chalifour, Vincent 1 Chang, Jen-Hsu 1 Chneguir, S. 1 Choque Rivero, Abdon Eddy 1 Chou, Chung-I 1 Clarkson, Peter A. 1 Conti, Riccardo 1 Contreras-Astorga, Alonso 1 Cunden, Fabio Deelan 1 Curbera, Guillermo P. 1 del Olmo, Mariano A. 1 Demina, Maria V. 1 Dimitrov, Dimitar K. 1 Domínguez de la Iglesia, Manuel 1 Đurić, Nebojša 1 Escobar-Ruiz, Mauricio A. 1 Eslahchi, Mohammad Reza 1 Fedorov, Yuri N. 1 Fehér, László Gy. 1 Feigin, Misha V. ...and 83 more Authors
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#### Cited in 56 Serials

 68 Journal of Mathematical Physics 18 Journal of Approximation Theory 10 Journal of Mathematical Analysis and Applications 8 Journal of Nonlinear Mathematical Physics 6 Letters in Mathematical Physics 5 International Journal of Modern Physics A 5 Theoretical and Mathematical Physics 5 Annals of Physics 5 Integral Transforms and Special Functions 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Journal of Physics A: Mathematical and Theoretical 3 Communications in Mathematical Physics 3 Physica D 2 Modern Physics Letters A 2 Physics Letters. A 2 Applied Mathematics and Computation 2 Studies in Applied Mathematics 2 Constructive Approximation 2 Mathematical Physics, Analysis and Geometry 2 Journal of High Energy Physics 2 Annales Henri Poincaré 2 International Journal of Geometric Methods in Modern Physics 2 Advances in High Energy Physics 1 International Journal of Modern Physics B 1 Journal of Engineering Mathematics 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Nuclear Physics. B 1 Physics Reports 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Proceedings of the American Mathematical Society 1 Advances in Applied Mathematics 1 Applied Mathematics and Mechanics. (English Edition) 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 SIAM Journal on Mathematical Analysis 1 Indagationes Mathematicae. New Series 1 Experimental Mathematics 1 Journal of Mathematical Sciences (New York) 1 Journal of Difference Equations and Applications 1 Novi Sad Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Regular and Chaotic Dynamics 1 Communications in Nonlinear Science and Numerical Simulation 1 Biostatistics 1 Qualitative Theory of Dynamical Systems 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Advances in Mathematical Physics 1 Iranian Journal of Mathematical Sciences and Informatics 1 Annalen der Physik 1 ISRN Mathematical Physics
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#### Cited in 37 Fields

 104 Special functions (33-XX) 93 Quantum theory (81-XX) 48 Ordinary differential equations (34-XX) 48 Harmonic analysis on Euclidean spaces (42-XX) 34 Dynamical systems and ergodic theory (37-XX) 27 Partial differential equations (35-XX) 24 Mechanics of particles and systems (70-XX) 11 Real functions (26-XX) 11 Numerical analysis (65-XX) 9 Difference and functional equations (39-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Functions of a complex variable (30-XX) 6 Nonassociative rings and algebras (17-XX) 5 Operator theory (47-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Field theory and polynomials (12-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Approximations and expansions (41-XX) 4 Differential geometry (53-XX) 3 Combinatorics (05-XX) 3 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 2 Relativity and gravitational theory (83-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX)