# School of Mathematics

## Dr Vladimir V Kisil

Reader of Applied Analysis

Pure Mathematics

### Contact details

Room: PRD 9.321

Tel: +44 (0)113 3435173

Email: V.Kisil @ leeds.ac.uk

### Keywords

Symmetry

Group

Analytic

Hypercomplex

Analysis

Quantum

Operator

Spectrum

## 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)

## Publications

**Kisil VV** Poincaré extension of Möbius transformations *Complex Variables and Elliptic Equations*, **62**, 1221-1236, 2017

DOI:10.1080/17476933.2016.1250399

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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

DOI:10.1007/978-3-319-12577-0_64

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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

DOI:10.15352/bjma/1396640061

**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

DOI:10.1007/s00006-012-0373-1

**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

DOI:10.1007/978-3-0348-0417-2

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**Kisil VV** Operator Covariant Transform and Local Principle *Journal of Physics A: Mathematical and Theoretical*, **45**, 2012

DOI:10.1088/1751-8113/45/24/244022

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**Kisil VV** Hypercomplex Representations of the Heisenberg Group and Mechanics *International Journal of Theoretical Physics*, **51**, 964-984, 2012

DOI:10.1007/s10773-011-0970-0

**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

DOI:10.1088/1742-6596/284/1/012038

**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

DOI:10.3842/SIGMA.2010.076

**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

DOI:10.1209/0295-5075/89/50005

**Kisil VV** Computation and Dynamics: Classical and Quantum *AIP Conference Proceedings*, **1232**, 306-312, 2010

DOI:10.1063/1.3431506

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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

DOI:10.1063/1.2747722

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

DOI:10.1007/s00006-006-0017-4

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

DOI:10.1209/epl/i2005-10324-7

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

DOI:10.1007/s00006-005-0012-1

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

DOI:10.1016/S0034-4877(05)80068-0

**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

DOI:10.1088/0305-4470/37/1/013

**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 theory*The 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 Orbits*GROUP 24: Physical and Mathematical Aspects of Symmetries 2003

**Kisil V ** *Meeting Descartes and Klein somewhere in noncommutative space*International 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

DOI:10.1007/s00026-002-8029-9

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**Kisil V ** *Tokens: an algebraic construction common in combinatorics, analysis, and physics*Ukr. Math. Congress-2001, 146-155 2002

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**Kisil V ** *Two Slits Interference Is Compatible with Particles' Trajectories*Quantum 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

DOI:10.1023/A:1013269432516

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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

DOI:10.1002/(SICI)1099-1476(19990310)22:4<353::AID-MMA44>3.0.CO;2-#

**Kisil V** Relative Convolutions I: Properties and Applications *Advances in Mathematics*, **147**, 35-73, 1999

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**Kisil V** Analysis in R^{1.1}or 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

DOI:10.1007/BF02524486

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**Prezhdo OV, Kisil VV** Mixing quantum and classical mechanics *Physical Review A*, **56**, 162-175, 1997

DOI:10.1103/PhysRevA.56.162

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

DOI:10.1002/(SICI)1099-1476(199706)20:9<745::AID-MMA878>3.0.CO;2-7

**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

DOI:10.1002/(SICI)1099-1476(19960525)19:8<593::AID-MMA783>3.0.CO;2-#

**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*

DOI:10.1002/(SICI)1099-1476(19990310)22:4<353::AID-MMA44>3.3.CO;2-R

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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*

DOI:10.7546/giq-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 Admissibility*in "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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