List of Publications

Vladimir V.Kisil

This is the complete List of publications. It is also available as a PDF file. Hyperlinks are provided whenever possible. See also my Eprints at and Google-Scholar profile

  1. The research monograph:
    V.V. Kisil, Geometry of Möbius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL(2,R), Imperial College Press, 2012.
  2. Published Papers (in Refereed Journals)
    1. V.V. Kisil, Two-sided Convolution Operators Algebra on the Heisenberg Group, Dokl. Acad. Nauk. SSSR, v. 325(1992), no. 1, p. 20–23,(Russian, translated in Russ. Acad. of Sci. Doklady, Math, v. 46(1993), pp. 12–16). MR # 93j:22018. Zbl # 801.47037.
    2. V.V. Kisil, On Pseudodifferential Operators Algebra on the Heisenberg Group, Sibirsk. Mat. Zh. 34(1993), no. 6, pp. 75–85. (Russian, translated in Siberian Math. J., v. 34(1993), no. 3, pp. 1066–1075). MR # 95a:47053. Zbl # 811.58058.
    3. V.V. Kisil, Local Properties of Convolution Operators with Singular Kernels on the Heisenberg Group, Mat. Zam., 56 (1994), N 2, pp. 41–55, (Russian, translated in Math. Notes 56(1995), no. 1–2, pp. 790–800). MR # 95j:22019. Zbl # 841.43020.
    4. V.V. Kisil, Spectrum of the Algebra Generated by Two-Sided Convolutions on the Heisenberg Group and Operators of Multiplication by Continuous Functions, Dokl. Akad. Nauk, v. 337(1994), no. 4, pp. 439–441 (Russian, translated in Russ. Acad. of Sci Doklady, Math, v. 50(1995), no. 1, pp. 92–97). MR # 95j:22019. Zbl # 853.22005.
    5. V.V. Kisil and O.P. Pilipenko, The Artificial Intelligence: Structure and Examining, Science and Science of Science, v. 1–2(1995), no. 7, pp. 73–77.
      E-print: HTML
      E-print: PDF
    6. V.V. Kisil, Connection between Two-Sided and One-Sided Convolution Type Operators on Non-Commutative Groups, Integr. Equat. Oper. Th., v. 22(1995), no. 3, pp. 317–332. MR # 96d:44004. Zbl # 840.43020.
    7. V.V. Kisil. Connection between Different Function Theories in Clifford Analysis. Advances in Applied Clifford Algebras, v. 5(1995), no. 1, p. 63–74. MR # 97a:30061. Zbl # 960.24964. arXiv:funct-an/9501002.
    8. N. Vasilevski, V. Kisil, E. Ramírez de Arellano, R. Trujillo, The Toeplitz Operators with Discontinuous Pre-Symbols in the Fock Space, Dokl. Acad. Nauk. of Russia, v. 345(1995), no. 2, pp. 153–155 (Russian). MR # 97b:47022. Zbl # 980.09694.
    9. V.V. Kisil. Integral Representations and Coherent States. Bulletin of the Belgian Mathematical Society, v. 2(1995), No 5, pp. 529–540. MR # 97b:22012. Zbl # 844.32005.
    10. V.V. Kisil, Plain Mechanics: Classical and Quantum, J. of Natural Geometry, v. 9(1996), no. 1, pp. 1–14. MR # 96m:81112. Zbl # 836.22010. arXiv:funct-an/9405002.
    11. V.V. Kisil, Local Algebras of Two-Sided Convolution on the Heisenberg Group, Mat. Zam., v. 59(1996), No 3, pp. 370–381, (Russian). MR # 97h:22006. Zbl # 876.22012.
    12. V.V. Kisil, Möbius Transformations and Monogenic Functional Calculus, Electron. Res. Announc. Amer. Math. Soc., v. 2(1996), No 1, pp. 26–33. MR # 98a:47018. Zbl # 869.47013.
    13. V.V. Kisil, Construction of Integral Representations in Spaces of Analytic Functions, Dokl. Acad. Nauk. of Russia, v. 350(1996), No 4, pp. 446–448 (Russian). MR # 98d:46027. Zbl # 980.25715.
    14. V.V. Kisil and E. Ramírez de Arellano. The Riesz-Clifford Functional Calculus for Several Non-Commuting Operators and Quantum Field Theory, Math. Methods Appl. Sci., 19(1996), No 8, pp. 593–605.
      MR # 97h:47009. Zbl # 853.47012 arXiv:funct-an/9502006.
    15. V.V. Kisil, E. Ramírez, A Functional Model for Quantum Mechanics: Unbounded Operators, Math. Methods Appl. Sci., 20(1997), No 9, pp. 745–757. MR # 98f:47028. Zbl # 970.31204.
    16. O.P. Prezhdo and V.V. Kisil, Mixing Quantum and Classic Mechanics, Phys. Rev. (A), 56(1997), No 1, pp. 162–176. MR # 99j:81010 arXiv:quant-ph/9610016.
    17. V.V. Kisil. Relativistic Quantization and Improved Equation for a Free Relativistic Particle, Physics Essays, 11(1998), No 1, pp. 69–80. arXiv:quant-ph/9502022. MR # 99c:81117.
    18. V.V. Kisil, A Paley–Wiener Theorem for Nilpotent Lie Groups, Ukr. Math. J., 50(1998), No 11, pp. 1564–1566.
      arXiv:funct-an/9602007. MR # 2000m:22010. Zbl # 934.43003.
    19. J. Cnops and V.V. Kisil, Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics, Math. Methods Appl. Sci., 22(1999), no. 4, pp. 353–373. arXiv:math/9806150. MR # 2000b:81044. Zbl # 923.22003.
    20. V.V. Kisil, Relative Convolutions I. Properties and Applications, Advances in Mathematics, 147(1999), no. 1, pp. 35–73. arXiv:funct-an/9410001. MR # 2001h:22012. Zbl # 933.43004.
    21. V.V. Kisil, Wavelets in Banach Spaces, Acta Appl. Math. 59(1999), no. 1, pp. 79–109. arXiv:math/9807141. MR # 2001c:43013. Zbl # 955.42024.
    22. V.V. Kisil, Analysis in R1,1 or the Principal Function Theory, Complex Variables Theory Appl., 40(1999), no. 2, pp. 93–118. arXiv:funct-an/9712003. MR # 2000k:30078. Zbl # 980.36633.
    23. V.V. Kisil, The Umbral Calculus and Cancellation Semigroup Algebras, Zeitschrift für Analysis und ihre Anwendungen, 19(2000), no. 2, pp. 315–338.
      arXiv:funct-an/9704001. MR # 2001g:05017. Zbl # 0959.43004.
    24. V.V. Kisil, Quantum and Classic Brackets, Int. J. Theor. Phys., 41(2002), no. 1, pp. 63–77. arXiv:math-ph/0007030. MR # 2003b:81105.
    25. V.V. Kisil, Polynomial Sequences of Binomial Type and Path Integrals, Ann. of Combinatorics, 6(2002), no. 1, pp. 45–56. arXiv:math/9808040. MR # 2003e:05010. Zbl # 1009.05013.
    26. V.V. Kisil, p-Mechanics as a Physical Theory: an Introduction, J. Phys. A, 37(2004), no. 1, pp. 183–204. arXiv:quant-ph/0212101. MR # 2005c:81078. Zbl # 1045.81032.
    27. V.V. Kisil, An Example of Clifford Algebras Calculations with GiNaC., Advances in Applied Clifford Algebras, 15(2005), no. 2, pp. 239–269. arXiv:cs.MS/0410044.
    28. V.V. Kisil, Monogenic Calculus as an Intertwining Operator, Bull. Belg. Math. Soc. Simon Stevin, 11(2005), no. 5, pp. 739–757. arXiv:math.FA/0311285. MR # 2006a:47025.
    29. V.V. Kisil, p-Mechanics and field theory, Rep. Math. Phys. 56 (2005), no. 2, 161–174, arXiv:quant-ph/0402035. MR # 2006h:53104.
    30. V.V. Kisil, A quantum-classical brackets from p-mechanics, Europhys. Lett. 72(2005) no. 6, 873–879, arXiv:quant-ph/0506122. MR # 2006k:81134.
    31. V.V. Kisil, Fillmore–Springer–Cnops Construction Implemented in GiNaC, Advances in Applied Clifford Algebras, 17(2007), no. 1, pp. 59–70, arXiv:cs.MS/0512073.
    32. V.V. Kisil, Two-Dimensional Conformal Models of Space-Time and Their Compactification, J. Math. Phys, 48(2007), no. 7, 073506. arXiv:math-ph/0611053.
    33. V.V. Kisil, Starting with the group SL(2,ℝ), Notices Amer. Math. Soc., 54(2007), no. 11, pp. 1458–1465. arXiv:math.GM/0607387.
    34. V.V. Kisil, Comment on “Do we have a consistent non-adiabatic quantum-classical mechanics?” by Agostini F. et al., Euro Phys. Lett. EPL, 89 (2010) 50005, arXiv:0907.0855, doi: 10.1209/0295-5075/89/50005.
    35. V.V. Kisil, Erlangen Program at Large—1: Geometry of Invariants, SIGMA 6 (2010), 076, 45 pages, arXiv:math.CV/0512416.
    36. V.V. Kisil, Computation and Dynamics: Classical and Quantum, AIP Conference Proceedings, v. 1232 (2010), pp. 306–312. doi: 10.1063/1.3431506, arXiv:0909.1594.
    37. V.V. Kisil, Covariant Transform, J. Phys.: Conf. Ser., v. 284 (2011), p. 012038. doi: 10.1088/1742-6596/284/1/012038, arXiv:1011.3947.
    38. V.V. Kisil, Erlangen Programme at Large 3.2: Ladder Operators in Hypercomplex Mechanics, Acta Polytechnica, v. 51 (2011), n. 4, pp. 44–53, arXiv:1103.1120.
    39. V.V. Kisil, Hypercomplex Representations of the Heisenberg Group and Mechanics, Internat. J. Theoret. Phys., v. 51(2012), no. 3, pp. 964–984, doi: 10.1007/s10773-011-0970-0, arXiv:1005.5057.
    40. V.V. Kisil, Operator Covariant Transform and Local Principle, J. Phys. A: Math. Theor. 45 (2012) 244022. doi: 10.1088/1751-8113/45/24/244022. arXiv:1201.1749.
    41. V.V. Kisil, Induced Representations and Hypercomplex Numbers, Adv. Appl. Clifford Algebras, 23 (2013), no. 2, pp. 417–440. doi: 10.1007/s00006-012-0373-1, arXiv:0909.4464.
    42. V.V. Kisil, Is Commutativity of Observables the Main Feature, which Separate Classical Mechanics from Quantum?, Izvestiya Komi nauchnogo centra UrO RAN, 3 (2012), n. 11, p. 4–9. arXiv:1204.1858.
    43. V.V. Kisil, Calculus of Operators: Covariant Transform and Relative Convolutions, Banach J. Math. Anal., 8(2014), no. 2., pp.156–184, arXiv:1304.2792. On-line.
    44. V.V. Kisil, The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform, Eurasian Math. J., 5 (2014), no. 1, pp. 95–121. arXiv:1209.5072. On-line.
    45. V.V. Kisil, Remark on Continued Fractions, Moebius Transformations and Cycles, Izvestiya Komi nauchnogo centra UrO RAN, 25 (2016), p. 11–17. arXiv:1412.1457.
    46. V.V. Kisil, Poincaré Extension of Möbius Transformations, Compl. Var. Ell. Eq.,62 (2017), no. 9, pp. 1221–1236. doi:10.1080/17476933.2016.1250399. arXiv:1507.02257.
    47. F. Almalki and V.V. Kisil, Geometric Dynamics of a Harmonic Oscillator, Arbitrary Minimal Uncertainty States and the Smallest Step 3 Nilpotent Lie Group, J. Phys. A: Math. Theor, 52(2019), 025301, on-line, arXiv:1805.01399.
    48. V.V. Kisil, An Extension of Mobius–Lie Geometry With Conformal Ensembles of Cycles and Its Implementation in a GiNaC Library, Proc. Int. Geom. Cent., 11(2018), n.3, pp.45–67, on-line. arXiv:1512.02960
  3. Other Papers Published in Refereed Editions
    1. V.V. Kisil, Some Subjective Notes about Mathematical Simulation of Social Systems, in K.G. Troitzsch ed., Catastrophe, Chaos and Self-Organization in Social System: The proceeding of Seminar on Catastrophic Phenomena in Soviet Society and Self-organization in Social Processes, Kiev, 7–10 September, 1992, Universität Koblenz-Landau, Koblenz, 1993, pp. 3–10.
      E-print: PDF
      E-print: HTML
    2. V.V. Kisil, Clifford Valued Convolution Operator Algebras on the Heisenberg Group, in F. Brackx et. al. (eds. ), Clifford Algebras and Applications in Mathematical Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 287–294.
      Zbl # 832.15016.
    3. V.V. Kisil and O.P. Pilipenko, Verifying Artificial Intelligence, in S. Raczynski, Computer Simulation and Artificial Intelligence, Universidad Panamericana, Mexico, 1994, pp. 8–11.
    4. V.V. Kisil. Quantum Probabilities and Non-Commutative Fourier Transform on the Heisenberg Group. In Nigel Kalton, Elias Saab, and Montgomery-Smith editors, Interaction between Functional Analysis, Harmonic Analysis and Probability, Lect. Notes in Pure and Applied Mathematics, chapter 24, pp. 255–266, Marcel Dekker, Inc., New York, 1995. MR # 97b:81060. Zbl # 842.22020.
    5. V.V. Kisil and M.V. Kuzmin, Informational Systems with Structures Simulating Their Contents. In Stanislav Raczynski, editor, III Conference on Computer Simulation, Proceedings. Universidad Panamericana, México, 1995, pp. 14–20.
      E-print: HTML
      E-print: PDF
    6. V.V. Kisil, Towards to Analysis in Rp,q, in W. Sprössig and K. Gürlebeck eds., Proceedings of the Symposium “Analytical and Numerical Methods in Quaternionic and Clifford Analysis”, Seiffen, 1996, pp. 95–100, arXiv:1811.12746. Zbl # 882.30030.
    7. V.V. Kisil, How Many Essentially Different Function Theories Exist?, in V. Dietrich, K. Habetha, and G. Jank (eds): Clifford algebras and their application in mathematical physics. Aachen 1996. Kluwer Academic Publishers, 1998, pp. 175-184. E-print: clf-alg/kisi9602. MR # 99g:30057. Zbl # 980.29881.
    8. V.V. Kisil, Harmonic Analysis and Localization Technique, Odessa University Herald, 3(1998), pp. 60–63. arXiv:math/9902012.
    9. V.V. Kisil. A Function Theory in R1,1. in J. Ryan and D. Struppa, eds., Dirac Operators in Analysis (Newark, DE, 1997), number 394 in Pitman Research Notes in Mathematics. Pitman, Boston, pp. 176–190, 1998. arXiv:funct-an/9712003. MR # 2002e:30041.
    10. V.V. Kisil, Two Approaches to Non-Commutative Geometry, in H. Begehr, O. Celebi, and W. Tutschke, eds., Complex Methods for Partial Differential Equations, chapter 14, pages 219–248. Kluwer Academic Publishers, Netherlands, 1999. The paper won Essay Competition on ICMP2000, London, UK. arXiv:funct-an/9703001. MR # 2001a:01002. Zbl # 958.46040.
    11. V.V. Kisil, Wavelet Transform of Operators and Functional Calculus, in H. Begehr, O. Celebi, and W. Tutschke, eds., Complex Methods for Partial Differential Equations, chapter 21, pages 325–338. Kluwer Academic Publishers, Netherlands, 1999.
      arXiv:math/9807141. MR # 2001f:43011. Zbl # 941.43002.
    12. V.V. Kisil, Nilpotent Lie Groups in Clifford Analysis: Five Directions for Research, in F. Brackx, J.S.R. Chisholm, and V. Souček, eds., Clifford Analysis and Its Applications, pages 135–142. Kluwer Academic Publishers, Netherlands, 2001.
      arXiv:math-ph/0009013. MR # 2003b:30059. Zbl # 1005.22003.
    13. V.V. Kisil, Two Slits Interference Is Compatible with Particles’ Trajectories, in A. Khrennikov, ed., Quantum Theory: Reconsideration of Foundations, Växjö University Press, pages 215–226, 2002. arXiv:quant-ph/0111094.
    14. V.V. Kisil, Meeting Descartes and Klein somewhere in a noncommutative space, Highlights of Mathematical Physics (A. Fokas, J. Halliwell, T. Kibble, and B. Zegarlinski, eds.), AMS, 2002, pp. 165–189. arXiv:math-ph/0112059. MR # 2005b:43015
    15. V.V. Kisil, Tokens: an algebraic construction common in combinatorics, analysis, and physics, Functional Analysis: Proc. of the Ukrainian Math. Congress-2001, Kiev: Inst. of Math. of NAS of Ukraine, 2002, p 146–155. arXiv:math.FA/0201012.
    16. V.V. Kisil, p-Mechanical Brackets and Method of Orbits, in GROUP 24: Physical and Mathematical Aspects of Symmetries: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15-20 July 2002 (Eds. J.–P. Gazeau et al), Institute of Physics Conference Series, v. 173, Institute of Physics, 2003.
    17. A. Brodlie and V. V. Kisil, Observables and states in p-mechanics, Advances in Mathematics Research, V, Nova Sci., 2003, pp. 101–136. arXiv:quant-ph/0304023. MR # 2117375.
    18. V.V. Kisil, p-Mechanics and De Donder–Weyl theory, The Fifth International Conference “Symmetry in Nonlinear Mathematical Physics”, Proc. of Institute of Mathematics of NAS of Ukraine, v. 50 (part 3), 2004, pp. 1108–1115. arXiv:quant-ph/0306101. MR # 2005e:81116.
    19. V.V. Kisil, Spectrum as the Support of Functional Calculus, in “Functional Analysis and its Applications” (V. Kadets and W. Zelazko, eds), Math. Studies series., v. 197, Elsevier Science Publishers, North-Holland, 2004, pp. 133–142. arXiv:math.FA/0208249. MR # 2005k:47038.
    20. V.V. Kisil and D. Biswas, Elliptic, parabolic and hyperbolic analytic function theory–0: Geometry of domains, In Complex Analysis and Free Boundary Flows, volume 1 of Trans. Inst. Math. of the NAS of Ukraine, pages 100–118, 2004. arXiv:math.CV/0410399.
    21. V.V. Kisil, Fillmore–Springer–Cnops Construction Implemented in GiNaC, in “Proceedings 17th International Conference on the Applications of Computer Science and mathematics in Architecture and Civil Engineering” (K. Gürlebeck, C. Könke, eds), Bauhaus-Universtät Weimar, 2006. arXiv:cs.MS/0512073
    22. V.V. Kisil, 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, pp. 219–225 arXiv:0911.4701.
    23. V.V. Kisil, Erlangen Program at Large—2: Inventing a Wheel. The Parabolic One, In Complex Analysis and Free Boundary Flows, volume 7, number 2 of Trans. Inst. Math. of the NAS of Ukraine, pages 89–98, 2010, arXiv:0707.4024.
    24. V.V. Kisil, Erlangen programme at large: an Overview. In S.V. Rogosin and A.A. Koroleva (eds.) Advances in applied analysis, pages 1–94, Birkhäuser Verlag, Basel, 2012. doi: 10.1007/978-3-0348-0417-2_1. arXiv:1106.1686.
    25. V.V. Kisil, Boundedness of Relative Convolutions on Nilpotent Lie Groups, Zb. Pr. Inst. Mat. NAN Ukr. (Proc. Math. Inst. Ukr. Ac. Sci.), 2013 (10), n. 4–5, pp. 185–189. arXiv:1307.3882
    26. V.V. Kisil, Uncertainty and Analyticity, in V.V. Mityushev(eds.), Current Trends in Analysis and Its Applications, pp 583–590, 2015, Springer. arXiv:1312.4583.
    27. V.V. Kisil, Symmetry, Geometry, and Quantization with Hypercomplex Numbers, In Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka, editors, Geometry, integrability and quantization XVIII, pp. 11–76. Bulgar. Acad. Sci., Sofia, 2017. arXiv:1611.05650.
    28. V.V. Kisil, Möbius–Lie Geometry and Its Extension, In Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka, editors, Geometry, integrability and quantization XX, pp. 13–61. Bulgar. Acad. Sci., Sofia, 2019. arXiv:1811.10499.
  4. E-prints (papers and lecture notes)
    1. V.V. Kisil, Reflection Processes and Selforganization of Complex Systems, accepted for publication by Science and Science of Science, but will never be published due to local hardships (Russian). E-print: HTML and E-print: PDF.
    2. B.A. Veitsman, V.V. Kisil, Dialog-2: About Higher Education, Computerra, 35(1999), (Russain).
    3. V.V. Kisil, Spaces of Analytic Functions and Wavelets, PG lecture notes, 2000.
    4. V.V. Kisil, Wavelets in Applied and Pure Maths, PG lecture notes, 2003.
    5. V.V. Kisil, Erlangen program for geometry and analysis: SL2(R) case study, PG lecture notes, 2009–2018. E-print:
    6. V.V. Kisil and others, Elementary Integral Calculus, College&UG lecture notes, 2018.
    7. V.V. Kisil and others, Numbers and Vectors, UG lecture notes, 2016.
    8. V.V. Kisil and others, Introductory Functional Analysis, UG lecture notes, 2018.
  5. Preprints
    1. V.V. Kisil, E. Ramírez de Arellano, R. Trujillo, and N.L. Vasilevski. Toeplitz operators with discontinuous presymbols on the Fock space. Reporte Interno # 155, Departamento de Matemáticas, CINVESTAV del I.P.N., Mexico City, 1994.
    2. V.K. Kharchenko, V.V. Kisil, The Topological Extension of a Differential Calculus, 1995.
    3. V.V. Kisil and J. Reid, Conformal Parametrisation of Loxodromes by Triples of Circles, 2018. arXiv:1802.01864.

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