Dr Kristian Evans

Associate Professor, Mathematics

k.evans@swansea.ac.uk

Fluent Welsh Speaker

Available For Postgraduate Supervision

About

My research interests lie in Analysis and Probability, in particular in pseudo-differential operators and Levy-type processes. I am co-author (with Niels Jacob) of a series of Analysis textbooks, entitled A Course in Analysis. In recent years, I have enjoyed developing new Statistics teaching provision in the Mathematics Department, however I have also taught a wide range of topics in Mathematics, including Complex Analysis. I have a genuine interest in teaching in an engaging and inclusive way and I like to share good practice where appropriate. I am also the Programme Director for Mathematics.

Publications

Research Highlights

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
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). 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
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
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
Evans, K. (2018). An Overview of the Pingo Audience Response System in Undergraduate Mathematics and Statistics Teaching. MSOR Connections, 17(1), 25
https://doi.org/10.21100/msor.v17i1.828, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa45005
https://journals.gre.ac.uk/index.php/msor/article/view/828
Jacob, N. & Evans, K. (2018). A Course in Analysis Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43213
https://www.worldscientific.com/worldscibooks/10.1142/11078
Jacob, N. & Evans, K. (2017). A Course in Analysis Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35868
http://www.worldscientific.com/worldscibooks/10.1142/10548
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 Vol. I: Introductory Calculus, Analysis of Functions of One Real Variable
https://doi.org/10.1142/9625, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23505
http://dx.doi.org/10.1142/9625

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
Evans, K. (2018). An Overview of the Pingo Audience Response System in Undergraduate Mathematics and Statistics Teaching. MSOR Connections, 17(1), 25
https://doi.org/10.21100/msor.v17i1.828, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa45005
https://journals.gre.ac.uk/index.php/msor/article/view/828
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
Evans, K., Jacob, N., & Morris, O. (2014). On a class of Pseudo-Differential Operators on R^n x Z^m generating Feller Semigroups. Rev. Roumaine Math. Pures Appl., 59, 55-75.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19855
Evans, K. & Jacob, N. (2012). Q-matrices as pseudo-differential operators with negative definite symbols. Mathematische Nachrichten, 286(5-6), 631-640.
https://doi.org/10.1002/mana.201100217, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19853
Neate, A. & Evans, K. (2012). Mathematical Presentation and Communication Skills within the Core Curriculum. Further Work Developing Graduate Skills in HE Mathematics Programmes, 12-13.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43214
http://www.mathcentre.ac.uk/resources/uploaded/furthergradskills.pdf
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
Evans, K. & Jacob, N. (2007). Feller Semigroups Obtained by Variable Order Subordination. Revista Matemática Complutense, 20(2), 293-307.
https://doi.org/10.5209/rev_REMA.2007.v20.n2.16482, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19852
http://www.springer.com/mathematics/journal/13163

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. (2018). A Course in Analysis Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43213
https://www.worldscientific.com/worldscibooks/10.1142/11078
Jacob, N. & Evans, K. (2017). A Course in Analysis Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35868
http://www.worldscientific.com/worldscibooks/10.1142/10548
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

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

Other Research Outputs

Jacob, N. & Evans, K. (2015). A Course in Analysis Vol. I: Introductory Calculus, Analysis of Functions of One Real Variable
https://doi.org/10.1142/9625, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23505
http://dx.doi.org/10.1142/9625

Taught Modules

MA-292 Statistical Data Analysis

This module concentrates on non-parametric statistics and techniques used to treat categorical data. In particular, the module covers a variety of statistical tests, criteria for choosing appropriate tests and the use of statistical software in order to deal with large data sets.
MA-301 Complex Analysis

The module approaches the theory of complex analytic functions; including concepts of Cauchy-Riemann equations, power series, Laurent series and residue calculus.
MAW301 Dadansoddi Cymhlyg

Mae'r modiwl hwn yn ystyried y theori o ffwythiannau analytig cymhlyg; gan gynnwys cysyniadau o hafaliadau Cauchy-Riemann, cyfresi pwer, cyfresi Laurent a chalcwlws gweddill.

Dr Kristian Evans

Email address

Welsh language proficiency

About

Publications

Research Highlights

All Research

Journal Articles

Authored Books

Conference Contributions

Other Research Outputs

Taught Modules

MA-292 Statistical Data Analysis

MA-301 Complex Analysis

MAW301 Dadansoddi Cymhlyg

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