Professor Neils Jacob

Professor Emeritus (Science)

Faculty of Science and Engineering

n.jacob@swansea.ac.uk

Office - 314
Third Floor
Computational Foundry
Bay Campus

About

In 2000 I was appointed to the Department of Mathematics in Swansea from which I have retired in 2020. During my time in Swansea, I was heavily involved in forming the School of Physical Sciences and later in establishing the College of Science, as I was much involved in creating and later running WIMCS, the Wales Institute of Mathematical and Computational Sciences. As one of Deputy Heads of the School of Physical Science, and later as Head of Department within the College of Science, I had for ca. 10 years responsibility for the Department of Mathematics.

Publications

Research Highlights

Jacob, N. & Bray, L. (2016). Some Considerations on the Structure of Transition Densities of Symmetric Levy Processes. Communications in Stochastic Analysis, 10(4), 405-420.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa30157
https://digitalcommons.lsu.edu/cosa/vol10/iss4/
Jacob, N., Evans, K., & Morris, O. (2014). On a class of pseudo-differential operators on R^n x Z^m generating Feller semigroups. Revue Roumaine de Mathematiques Pures et Appliquees, 59, 55-75.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23005
Jacob, N., Chen, Z., Takeda, M., & Uemura, T. (Eds.). (2015). Festschrift Masatoshi Fukushima. World Scientific.
https://doi.org/10.1142/9129, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23002
https://www.worldscientific.com/worldscibooks/10.1142/9129#t=toc
Jacob, N. & Evans, K. (2015). A Course in Analysis Volume I: Introductory Calculus, Analysis of Functions of One Real Variable World Scientific.
https://doi.org/10.1142/9625, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23001
https://www.worldscientific.com/worldscibooks/10.1142/9625
Jacob, N., Wang, Y., & Yuan, C. (2009). Stochastic differential delay equations with jumps, under nonlinear growth condition. Stochastics An International Journal of Probability and Stochastic Processes, 81(6), 571-588.
https://doi.org/10.1080/17442500903251832, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1062
Jacob, N., Wang, Y., & Yuan, C. (2009). Numerical Solutions of Stochastic Differential Delay Equations with Jumps. Stochastic Analysis and Applications, 27(4), 825-853.
https://doi.org/10.1080/07362990902976637, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1066
Farkas, W. & Jacob, N. (2001). Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions. Mathematische Nachrichten, 224(1), 75-104.
https://doi.org/10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1626
JACOB, N., TOKAREV, A., & Jacob, N. (2004). A PARAMETER-DEPENDENT SYMBOLIC CALCULUS FOR PSEUDO-DIFFERENTIAL OPERATORS WITH NEGATIVE-DEFINITE SYMBOLS. Journal of the London Mathematical Society, 70(3), 780-796.
https://doi.org/10.1112/S0024610704005769, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1627
Evans, K. & Jacob, N. (2011). Variable order subordination in the sense of Bochner and pseudo-differential operators. Mathematische Nachrichten, 284(8-9), 987-1002.
https://doi.org/10.1002/mana.200810246, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8059
Jacob, N. & Schilling, R. (2010). Extended L p Dirichlet Spaces. Around the Research of Vladimir Maz'ya I (pp. 221-238). Springer
https://doi.org/10.1007/978-1-4419-1341-8_9, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8060

All Research

Journal Articles

Evans, K., Fry, H., & Jacob, N. (2021). Fundamental solutions in $\psi$-Bessel potential spaces of certain generators of transient Lévy processes. Revue Roumaine Mathematiques Pures et Appliquees, 66(1), 157-177.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa55969
http://imar.ro/journals/Revue_Mathematique/php/2021/Rrc21_1.php
Evans, K. & Jacob, N. (2020). On Adjoint Additive Processes. Probability and Mathematical Statistics, 40(2), 205-223.
https://doi.org/10.37190/0208-4147.40.2.2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48685
https://www.math.uni.wroc.pl/~pms/publications.php?nr=40.2
Jacob, N. & Wang, F. (2018). Higher order eigenvalues for non-local Schrödinger operators. Communications on Pure & Applied Analysis, 17(1), 191-208.
https://doi.org/10.3934/cpaa.2018012, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa36033
Jacob, N. & Bray, L. (2016). Some Considerations on the Structure of Transition Densities of Symmetric Levy Processes. Communications in Stochastic Analysis, 10(4), 405-420.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa30157
https://digitalcommons.lsu.edu/cosa/vol10/iss4/
Evans, K., Jacob, N., & Shen, C. (2015). SOME FELLER SEMIGROUPS ON C_∞(R^n×Z^m) GENERATED BY PSEUDO-DIFFERENTIAL OPERATORS. Mathematika, 61(2), 402-413.
https://doi.org/10.1112/S002557931500011X, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22138
Jacob, N., Evans, K., & Morris, O. (2014). On a class of pseudo-differential operators on R^n x Z^m generating Feller semigroups. Revue Roumaine de Mathematiques Pures et Appliquees, 59, 55-75.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23005
Jacob, N., Knopova, V., Landwehr, S., & Schilling, R. (2012). A geometric interpretation of the transition density of a symmetric Lévy process. Science China Mathematics, 55(6), 1099-1126.
https://doi.org/10.1007/s11425-012-4368-0, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa14014
Evans, K. & Jacob, N. (2011). Variable order subordination in the sense of Bochner and pseudo-differential operators. Mathematische Nachrichten, 284(8-9), 987-1002.
https://doi.org/10.1002/mana.200810246, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8059
Jacob, N. & Schicks, M. (2010). Multiparameter Markov Process: Generators and associated martingales. Revue Roumaine Mathematiques Pures et Appliques, 55, 27-34.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8061
Jacob, N., Potrykus, A., Wu, J., Jacob, N., Potrykus, A., & Wu, J. (2010). Solving a non-linear stochastic pseudo-differential equation of Burgers type. Stochastic Processes and their Applications, 120(12), 2447-2467.
https://doi.org/10.1016/j.spa.2010.08.007, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8092
http://dx.doi.org/10.1016/j.spa.2010.08.007
Jacob, N., Wang, Y., & Yuan, C. (2009). Stochastic differential delay equations with jumps, under nonlinear growth condition. Stochastics An International Journal of Probability and Stochastic Processes, 81(6), 571-588.
https://doi.org/10.1080/17442500903251832, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1062
Jacob, N., Wang, Y., & Yuan, C. (2009). Numerical Solutions of Stochastic Differential Delay Equations with Jumps. Stochastic Analysis and Applications, 27(4), 825-853.
https://doi.org/10.1080/07362990902976637, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1066
Jacob, N., POTRYKUS, A., & Wu, J. (2008). SOLVING A NONLINEAR PSEUDO-DIFFERENTIAL EQUATION OF BURGERS TYPE. Stochastics and Dynamics, 08(04), 613-624.
https://doi.org/10.1142/s0219493708002482, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7451
http://dx.doi.org/10.1142/s0219493708002482
JACOB, N., TOKAREV, A., & Jacob, N. (2004). A PARAMETER-DEPENDENT SYMBOLIC CALCULUS FOR PSEUDO-DIFFERENTIAL OPERATORS WITH NEGATIVE-DEFINITE SYMBOLS. Journal of the London Mathematical Society, 70(3), 780-796.
https://doi.org/10.1112/S0024610704005769, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1627
Farkas, W. & Jacob, N. (2001). Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions. Mathematische Nachrichten, 224(1), 75-104.
https://doi.org/10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1626

Authored Books

Evans, K. & Jacob, N. (2020). A Course in Analysis Vol. V: Functional Analysis, Some Operator Theory, Theory of Distributions. World Scientific.
https://doi.org/https://doi.org/10.1142/11695, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53554
https://www.worldscientific.com/worldscibooks/10.1142/11695
Jacob, N. & Evans, K. (2016). A Course in Analysis. Vol II: Differentiation and Integration of Functions of Several Variables, Vector Calculus World Scientific.
https://doi.org/10.1142/10059, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa29669
http://www.worldscientific.com/worldscibooks/10.1142/10059
Jacob, N. & Evans, K. (2015). A Course in Analysis Volume I: Introductory Calculus, Analysis of Functions of One Real Variable World Scientific.
https://doi.org/10.1142/9625, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23001
https://www.worldscientific.com/worldscibooks/10.1142/9625

Book Chapters

Evans, K. & Jacob, N. (2022). Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators. In A.M. Candela, M. Cappelletti Montano, E. Mangino (Ed.), Trends in Mathematics (pp. 333-362). Springer International Publishing
https://doi.org/10.1007/978-3-031-20021-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64994
https://link.springer.com/chapter/10.1007/978-3-031-20021-2_17
Jacob, N. & Schilling, R. (2010). Extended L p Dirichlet Spaces. Around the Research of Vladimir Maz'ya I (pp. 221-238). Springer
https://doi.org/10.1007/978-1-4419-1341-8_9, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8060
Jacob, N., Potrykus, A., & Schicks, M. (2009). Operators associated with multi-parameter families of probability measures. In : Potential Theory and Stochastics in Albac 2007. The Aurel Cornea Memorial Volume. Ed. D.Bakry et al., Theta Series in Advanced Mathematics (pp. 157-172). Theta
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8062

Conference Contributions

Evans, K. & Jacob, N. (2022). On Non-negative Solutions to Space-Time Partial Differential Equations of Higher Order. In Springer Proceedings in Mathematics and Statistics (pp. 85-107). Springer Nature Singapore.
https://doi.org/10.1007/978-981-19-4672-1_6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59047

Edited Books

Jacob, N., Chen, Z., Takeda, M., & Uemura, T. (Eds.). (2015). Festschrift Masatoshi Fukushima. World Scientific.
https://doi.org/10.1142/9129, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23002
https://www.worldscientific.com/worldscibooks/10.1142/9129#t=toc