School of Mathematics

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Dr Vladimir V Kisil

Reader of Applied Analysis
Pure Mathematics

Contact details

Room: PRD 9.321
Tel: +44 (0)113 3435173
Email: V.Kisil @



Research interests

Applications of symmetries and group representations in geometry, complex analysis, operator theory, functional calculus and spectra. In particular:

* C*-algebras with symmetries, particularly algebra of convolutions and pseudo-differential operators on Lie groups and homogeneous spaces;

* Functional calculus of operators and associated notions of (joint) spectrum of operators;

* Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex, hypercomplex and Clifford analysis;

* Applications of coherent states, wavelet transform and group representations in quantum mechanics, foundations of quantum mechanics;

* Non-commutative geometry of homogeneous space based on the Erlangen programme;

* Cancellative semigroups and umbral-type calculus in combinatorics, mathematical physics and analysis.

Useful links

I put all my papers to the arXiv.
Information for Prospective Postgraduate Students
I obtained my both degrees from the Odessa University
My personal homepage

Current postgraduate students

Amerah Alameer (2014)
Amjad Alghamdi (2016)
Dale Hodgson (2016)
Khawlah Mustafa (2014)
Richard Whyman (2014)


Kisil VV Poincaré extension of Möbius transformations Complex Variables and Elliptic Equations, 62, 1221-1236, 2017
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Kisil VV Remark on Continued Fractions, Moebius Transformations and Cycles Izvestiya Komi nauchnogo centra UrO RAN, 11-11, 2016
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Kisil VV Uncertainty and analyticity In Current Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Kraków 2013, 583-590, 2015
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Kisil VV The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform Eurasian Mathematical Journal, 5, 95-121, 2014
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Kisil VV Calculus of Operators: Covariant Transform and Relative Convolutions Banach Journal of Mathematical Analysis, 8, 156-184, 2014

Kisil V Boundedness of relative convolutions on nilpotent Lie groups Zb. Pr. Inst. Mat. NAN Ukr., 10(2013), N 4-5, pp.185-189, 2013
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Kisil VV Induced Representations and Hypercomplex Numbers Advances in Applied Clifford Algebras, 23, 417-440, 2013

Kisil VV Classical/Quantum=Commutative/Noncommutative? Izvestiya Komi Nauchnogo Centra, 3, 4-9, 2012
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Kisil VV Erlangen Programme at Large: An Overview In Advances in Applied Analysis, 1-94, 2012
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Kisil VV Operator Covariant Transform and Local Principle Journal of Physics A: Mathematical and Theoretical, 45, 2012
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Kisil VV Hypercomplex Representations of the Heisenberg Group and Mechanics International Journal of Theoretical Physics, 51, 964-984, 2012

Kisil V Geometry of Mobius transformations: Elliptic, parabolic and hyperbolic actions of SL_2(R). London: Imperial College Press 2012
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Kisil VV Covariant Transform Journal of Physics: Conference Series, 284, 012038-012038, 2011

Kisil VV Erlangen Programme at Large 3.2: Ladder Operators in Hypercomplex Mechanics Acta Polytechnica, 51, 44-53, 2011
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Kisil VV Erlangen Program at Large-1: Geometry of Invariants Symmetry, Integrability and Geometry: Methods and Applications, 2010

Kisil VV Comment on“Do we have a consistent non-adiabatic quantum-classical mechanics?” by Agostini F. et al. EPL (Europhysics Letters), 89, 50005-50005, 2010

Kisil VV Computation and Dynamics: Classical and Quantum AIP Conference Proceedings, 1232, 306-312, 2010
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Kisil VV Erlangen Program at Large--2: Inventing a wheel. The parabolic one Trans. Inst. Math. of the NAS of Ukraine, 7, 89-98, 2010
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Kisil V Starting with the group SL(2,R) Notices of the American Mathematical Society, 54, 1-8, 2007
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Kisil VV Two-dimensional conformal models of space-time and their compactification Journal of Mathematical Physics, 48, 073506-073506, 2007

Kisil VV Fillmore–Springer–Cnops Construction Implemented in GiNaC Advances in Applied Clifford Algebras, 17, 59-70, 2007

Kisil VV A quantum-classical bracket from p -mechanics Europhysics Letters (EPL), 72, 873-879, 2005

Kisil* VV An example of Clifford algebras calculations with GiNaC Advances in Applied Clifford Algebras, 15, 239-269, 2005

Kisil VV p-Mechanics and field theory Reports on Mathematical Physics, 56, 161-174, 2005

Kisil VV Monogenic Calculus as an Intertwining Operator Bulletin of the Belgian Mathematical Society - Simon Stevin, 11, 739-757, 2005
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Kisil V Spectrum as the support of functional calculus In Functional Analysis and its Applications, 197, 133-142, 2004
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Kisil V, Biswas D Elliptic, parabolic and hyperbolic analytic function theory-0: Geometry of domains In Complex Analysis and Free Boundary Flows, 1, pp.100--118, 2004
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Kisil VV p -mechanics as a physical theory: an introduction Journal of Physics A: Mathematical and General, 37, 183-204, 2004

Kisil VV p-mechanical brackets and method of orbits Institute of Physics Conference Series, 173, 665-669, 2003
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Kisil V p-Mechanics and De Donder-Weyl theoryThe Fifth Int. Conf. "Symmetry in Nonlinear Mathematical Physics", 1108-1115 2003
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Brodlie AR, Kisil V Observables and states in p-mechanics In Advances in Mathematics Research, V, pp. 101--136, 2003
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Kisil V p-Mechanical Brackets and Method of OrbitsGROUP 24: Physical and Mathematical Aspects of Symmetries 2003

Kisil V Meeting Descartes and Klein somewhere in noncommutative spaceInternational Conference on Mathematical Physics (13th:2000:London, England), 165-189 2002
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Kisil V Polynomial sequences of binomial type path integrals Annals of Combinatorics, 6, 45-56, 2002
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Kisil V Tokens: an algebraic construction common in combinatorics, analysis, and physicsUkr. Math. Congress-2001, 146-155 2002
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Kisil V Two Slits Interference Is Compatible with Particles' TrajectoriesQuantum Theory: Reconsideration of Foundations, pp.215--226 2002
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Kisil V Quantum and Classic Brackets International Journal of Theoretical Physics, 41, 63-77, 2002
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Kisil V The Umbral Calculus and Cancellation Semigroup Algebras Zeitschrift fuer Analysis und Ihre Anwendungen, 19, 315-338, 2000
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Cnops J, Kisil VV Monogenic functions and representations of nilpotent Lie groups in quantum mechanics Mathematical Methods in the Applied Sciences, 22, 353-373, 1999

Kisil V Relative Convolutions I: Properties and Applications Advances in Mathematics, 147, 35-73, 1999
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Kisil V Analysis in R1.1or the Principal Function Theory Complex Variables: Theory and Application, 40, 93-118, 1999
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Kisil V Wavelets in Banach Spaces Acta Applicandae Mathematicae, 59, 79-109, 1999
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Kisil VV Paley-Wiener Theorem for Nilpotent Lie Groups Ukrainian Mathematical Journal, 50, 1786-1788, 1998
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Prezhdo OV, Kisil VV Mixing quantum and classical mechanics Physical Review A, 56, 162-175, 1997

Kisil VV, Ramírez de Arellano E A Functional Model for Quantum Mechanics: Unbounded Operators Mathematical Methods in the Applied Sciences, 20, 745-757, 1997

Kisil VV, Ramírez de Arellano E The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory Mathematical Methods in the Applied Sciences, 19, 593-605, 1996

Kisil VV Relativistic Quantization and Improved Equation for a Free Relativistic Particle Physics Essays, 11, 69-80, 1995
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Kisil VV No More Than Mechanics. I J. of Natural Geometry, v. 9 (1996), no. 1, pp. 1-14
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Kisil VV Connection between Different Function Theories in Clifford Analysis no., 1, 63-74,
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Cnops J, Kisil V Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics Math. Methods Appl. Sci., 22(1999), no. 4, pp. 353--373
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Kisil VV Harmonic Analysis and Localization Technique Odessa University Herald, v. 3 (1998), pp. 60--63
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Kisil VV Nilpotent Lie Groups in Clifford Analysis: Five Directions for Research F. Bracks et al. (eds.) Clifford Analysis and Its Applications, 135-141, 2001 Kluwer Academic Publishers
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Kisil VV Ensembles of Cycles Programmed in GiNaC arXiv
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Kisil VV Symmetry, Geometry, and Quantization with Hypercomplex Numbers Geometry, Integrability and Quantization, v. 18 (2017), 11-76
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Kisil VV Two Approaches to Non-Commutative Geometry H.~Begehr et al eds., Complex Methods for Partial Differential Equations, Ch~14, pp 219--248, Kluwer, 1999
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Kisil VV Analysis in $R^{1,1}$ or the Principal Function Theory Complex Variables Theory Appl., 40(1999), no.2, pp. 93--118
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Kisil VV Spaces of Analytical Functions and Wavelets--Lecture Notes.
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Kisil VV Wavelets Beyond Admissibilityin "Progress in Analysis and Its Applications - Proceedings of the 7th International ISAAC Congress'', (M. Ruzhansky, J. Wirth eds.), World Scientific, 2010, 219-225
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Kisil VV Erlangen Program at Large: Outline.
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Kisil V; Bauer C; Frink A; Kreckel R; Sheplyakov A GiNaC
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