Dr. V. Kannan

Publications

• V. Kannan and Pabitra Narayan Mandal, “Interval maps every point is eventually fixed” has been accepted for publication in “Proc. Mathematical Sciences -Indian Acad. Sci.”
• Modern Mathematics in Ancient India, Sixteen Samples from Sanskrit sources, Kannan, in the book “Mathematics and Reality”, Proceedings of a Conference at IIT Bhubaneswar, 378-395, (2018) Publ. Bhaktivedanta Institute, Kolkata.
• On the existence of compositional square roots, Kannan, Proceedings of a conference at Jadavpur University, 1-5 (2018)
• Reflexive cum co- reflexive subcategories in Topology, Math. Annallen, Kannan, 195, 168-174. (1972)
• A countable connected Urysohn space containing a dispersion point, Kannan, Proc. Amer. Math. Soc. 35, 289-290. (1972)
• Regularity and dispersion in countable spaces, Kannan and M.Rajagopalan, Duke Math. Jour. 39, 729-734. (1972)
• An extension that nowhere has the Frechet property, Kannan, Michigan Math. Jour. 20, 225-234(1973)
• On Countable locally connected spaces, Kannan and M.Rajagopalan, Colloq. Math. 29, 93-100. (1974)
• On Scattered Spaces, Kannan and M.Rajagopalan, Proc. Amer. Math. Soc. 43 , 402-408. (1974)
• A note on countable compact spaces, Kannan, Publ. Math. Debrecen 21, 113-114. (1974)
• A note on countably generated spaces, Kannan, Archive. Der. Math. 25, 42-43. (1974)
• Lattices of Hausdroff compactifications of a locally compact space, Kannan and T.Thrivikraman, Pacific Jour. Math. 57, 441-444. (1975)
• "Ordinal Invariants in Topology - I, on two questions of Arhangelskii and Franklin ", Kannan, General Topology and Applications 5, 269-296. (1975)
• Coreflective subcategories in Topology, (Summary of Doctoral Thesis), Kannan, Madurai University Journal, 5, 93-96. (1976)
• Constructions and Applications of Rigid Spaces - I, Kannan and M.Rajagopalan, Advances in Math. 29, 89-130. (1978)
• Scattered Spaces -II, Kannan and M.Rajagopalan, Illinois Jour. Math.21, 735-751. (1977)
• Constructions and Applications of Rigid Spaces - II, Kannan and M.Rajagopalan, Amer. Jour. Math. 100, 1139-1172. (1978)
• On a problem of Herrlich, Kannan, "Madurai University Journal, 6", 101-104. (1977)
• Constructions and Applications of Rigid Spaces - III, Kannan and M.Rajagopalan, Canadian Jour. Math. 30, 926-932. (1978)
• " Simpler Proofs - I, Independent Sets are thin", Kannan and A.K. Vijayakumar, Jour. Ind. Math. Soc.  42, 131-134. (1978)
• "Ordinal Invariants in Topology - II, Sequential order of compactifications", Kannan, Composito Math. 39, 247-262. (1979)
• Hereditarily locally compact spaces and simple extensions of discrete spaces, H. Herrlich, Kannan and M.Rajagopalan, Proc. Amer. Math. Soc. 77, 421-423. (1979)
• Every compact T5 sequential space is Frechet, Kannan, Fund. Mathematicae C VII, 85-90. (1980)
• The non - existence of invariant universal  sigma-finite measures on semigroups , Kannan and S.R.K. Raju, Proc. Amer. Math. Soc. 78, 482-484. (1980)
• "Simpler Proofs - 2, On a Set Theoretic Result of Mrowka", Kannan, Ind. Jour. Pure and Appl. Math. 12, 71-72. (1981)
• "Simpler Proofs - 4, On spaces with a unique compactification ", Kannan. Math. Student 48, 161-162. (1980)
• Ordinal Invariants in Topology, Kannan, Memoirs of the Amer. Math. Soc., 165 pages, (the entire volume No. 245). (1981)
• Properties that are productive, closed-hereditary and surjective , Kannan and T. Soundararajan, Topology and Applications 12, 141-146. (1981)
• Simpler Proofs 5-A characterization of inner product spaces, Kannan and S.R.K. Raju, Math. Today 1, 13-16. (1983)
• "Ordinal Invariants in Topology - III, Simplest compact spaces for sequential order", Kannan , Math. Today 1, 65-80. (1983)
• What is an ultra filter? , Kannan and M.Venkataraman, UGC Jour. Math. Edu., 1983
• A Problem in Approximation Theory, Kannan, Math. Student 54, 73-81. (1986)
• What is the maximum yield in the solid state cinnamic acid dimerisation?, Kannan and G.R. Desiraju, Proc. (Chem. Sci.) of the Indian Acad. Sci. 96, 351-362. (1986)
• Rogers-Ramanujan Identities: An elementary introduction, Kannan, UGC Jour. Math. Edu., 74-49. (1987)
• Two Applications of Banach-Stone Theorem, Kannan, Jour. Math. And Phys. Soc. 12, 227-239. (1987)
• Topological characterization of some countable Metric spaces, Kannan and M.Rajagopalan, Bulletin of U.M.I. (Italy), 351-357. (1987)
• Spaces every quotient of which is metrizable, Kannan, A.J. Jayanthan, Proc. Amer. Math. Soc. 103, 294-298. (1988)
• Converses of Lucas' s Theorem , Kannan, Math. Student 57, 53-58. (1989)
• Simultaneous Best Approximation by three polynomials , Kannan, S. Ravichandran, Jour. Approximation Theory 59, 258-266. (1989)
• Joins of Topologies homeomorphic to Rationals, Kannan, A.J. Jayanthan,  Jour. Australian Math. Soc. A47, 256-262. (1989)
• Theory of Dispersed Metric Spaces , Kannan, Bull. Allad. Math. Soc. 5, 79-109. (1990)
• Formulas for Functions, Kannan, Math. Student 64, 3-32. (1994)
• Cantor Set: from classical to modern , Kannan, Math. Student , 243-257. (1994)
• Some Selection Theorems, Kannan, Math. Student, 70-80. (1996)
• A generalization of Sarkovskii' s Theorem to higher dimensions ", Kannan P.V.S.P Saradhi and S.P. Sesha Sai, Jour. Nat. Acad. Math. 2, 69-82. 1997(appeared 1999)
• Properties of topologically transitive maps on the real line", Kannan, Anima Nagar and S.P. Sesha Sai, Real Anal. Exchange 27 , 2001
• Spaces admitting transitive maps, Kannan and Anima Nagar, Topology Proceedings 26(2001-2002), 2002
• Periodic Point Property, Kannan and P.V.S.P.Saradhi, Proc. of A.P. Academy of Sciences, Vol. 8, No. 3, 2004
• Some simple conditions implying topological transitivity for internal maps", Kannan, Anima Nagar and K. Srinivas, "Aequationes Mathematicae, 67", 2004
• Polynomials hardly commuting with increasing bijections, Kannan, B.Sankara Rao, I.Subramania Pillai and S.Niketa Salvi, Semigroup Forum, 76(i):124-132, ", 2008
• The Set of Periods of Periodic Points of a Linear Operator,  Kannan , K.Ali Akbar, Sharan Gopal and P.Chiranjeevi, Linear Algebra and Its Applications, 431, 241-246. (2009)
• Sets of all periodic points of a toral automorphism, K Ali Akbar,Kannan , I Subramania Pillai, B Sankara Rao J. Math. Anal. Appl. 366 , 367-371 (2010)
• Some families of subsets of N that arise in Topological Dynamics, Kannan, Bulletin of Kerala Mathematics Association, 2010.
• The set of  periods of periodic points of a toral automorphism, K Ali Akbar,Kannan,  I Subramania Pillai, B Sankara Rao Topology Proceedings, 37, 1-14. (2011)
• Sets of periods of dynamical systems, Kannan, Indian Journal of Pure and Applied Mathematics, Vol. 41, No.1, 225-240,  2010
• 63 kinds of subsets, Kannan,Sharan Gopal,  Bull. Kerala Math. Association 6, 121-130. (2010)
• The set of Dynamically special points,Kannan, Sankara Rao B, Subramania Pillai I, Aequationes Mathematicae (Austria) 82,  81-90. 2011
• Periodic Points and Periods for Operators on Hilbert Space, Kannan, Chiranjeevi and Sharan Gopal, Discrete and Continuous Dynamical Systems, Vol.33, 4233-4237, 2013.
• Homeomorphisms on compact metric spaces with finite derived length, Kannan, Sharan Gopal, Applied General Topology, 17, No2., 129-137. (2016)
• Dynamics on locally compact Hausdorff spaces, Topology Proceedings, Kannan, P. Chiranjeevi and M.Archana, 48 309-325. (2016)
• A Context-free language associated with interval maps, Kannan, M. Archana, Discrete Mathematics and Theoretical Computer Science, 2017.
• Intervals containing all periodic points, Real Analysis Exchange, Kannan, M. Archana, 41, 263-270. (2016)
• Study of Transitivity Through Steepness, Rakhee Basu, V.Kannan, Kunal Sannyasi and Nidhish Unnikrishnan, Topology Proceedings, 2017.
• (with) Functions Preserving Limit Superior, Rakhee Basu,V.Kannan, Kunal Sannyasi and Nidhish Unnikrishnan, College Mathematical Journal, 2017.

Conference Proceedings

• (with M. Rajagopalan) On rigidity and groups of homeomorphisms, General Topology and its relations to Modern Analysis and Algebra III, Proceedings of Third Prague Topology Symposium (1971). Publ (1972) 231-134.
• Ordinal Invariants in Topology - A summary, Kannan, Proceedings of Fourth Prague Topology Symposium (1976). Publ (1977) by Czech. Acad. Sci., 197-206.
• (with M. Rajagopalan) Hereditarily locally compact separable spaces, Proc. Berlin Symposium on Categorical Topology (1978) Springer Verlag Lecture Notes in Math. 719 (1979)185-195.
• Pairs of Topologies with same family of continuous self maps, Kannan, Proc. Berlin Symposium on Categorical Topology (1978) Springer Verlag Lecture Notes in Math. 719 (1979) 176-184.
• A classification theorem in Topology, Kannan , Proc. Conf. on general topology, set theory and modern analysis with applications, Univ. of California (1980) Academic Press (1981) 241-246.
• (with A.J. Jayanthan) Finite - to – one Quotients, Kannan Second Biennial Conf. Allahabad Math. Soc. (1990) 31-42.
• Linear Selection of Spectral elements , Kannan, Proc. Symposium on Operator Theory and functional Analysis, Publ. No. 18 (1990), Centre for Math. Studies, Trivendrum, 1-8.
• On Banach spaces of continuous functions, Kannan, Proc. Trends in Algebra and Topology, Madurai Kamaraj Univ. (1992) Publ. (1993) 87-94.
• Completeness and completion : Three different models, Kannan, Proc. Workshop on Speech Technology (1992) IIT Madras, 129-135.
• “(with Sharan Gopal)”, Four combinatorial problems in topology and dynamics, Kannan Proceedings of the National Seminar on Topology and Its Applications to Computer Science and Related Areas, Dept. of Mathematical Sciences, Kannur University, Nov. 25-26, 2009.
• “(with Sharan Gopal)”, A greedy algorithm hidden in sulbasutra, Kannan Proceedings of the National Workshop on Ancient Indian Mathematics, Rashtriya Sanskrit Vidyapeetha, during 20-24, September 2010.
• Eight important elementary results of Euler, V.Kannan, Proceedings of a National seminar at Sri Venkateshwara University, Tirupathi, 2011.
• (with Sharan Gopal), A greedy algorithm hidden in Sulbasutra, Proceedings of the National Workshop on Ancient Indian Mathematics, Rashtriya Sanskrit Vidyapeetha Publications Series -265, (2011) 17-26. Replace this repeated item by “Toral automorphisms”, Palghat.

Lectures Published

• Rivlin’s Problem in Approximation Theory, Kannan, Sectional Presidential Address, Eighty first session of Indian Science Congress Association, Jaipur (1994) 1-20.
• Convolutions, Kannan, Sixth Ramanujan Centenary Endowment Lecture, Anna University, Madras (1995) 1-24.
• Mathematics and Related Sciences in Vedas, Kannan, Yogakshema Trust, Chennai (1998) Republished : Hayoga Vedas (1999).
• Paracompact spaces, Kannan, "Prof. Afzal Ahmed Memorial Lecture, Ind. Jour. For the Advancement of Math. Exn. and Res.", 2003.
• "Three Ideas of Ulam, Kannan , Prof. Abdi Memorial Lectures", Published by Cochin University of Science and Technology along with other memorial lectures, 2003-2004.

Books

• (with Izhar Hussain, M.S. Rangachari and A.M. Vaidya) Text Books for Classes XI and XII, Kannan NCERT (1986) (4 volumes).
• (with J.N. Kapur, R.S.L. Srivastava, etc.) Text book : MTE-01, Calculus, V.Kannan, IGNOU (1990).

Videocassettes in Mathematics

• Parabolas, UGC Countrywide class room (1992).
• Compactness and continuity, Andhra Pradesh Open University (1994).
• (with W.W.Comfort) Krein-Milman Theorem, UGC Countrywide class room.
• (with Michel Waldshmidt) Squares, Cubes and Powers, UGC Countrywide class room.

Other published articles

• (with S.R.K. Raju) Structure of some Banach spaces, Lecture Notes of “a National Seminar on Mathematical Analysis and its Applications”, Ramanujan Institute of Advanced Study in Mathematics, University of Madras (1983).
• Mathematics in other sciences, Progressive Educational Herald (1987).
• Support required for books and journals in Mathematics, IMS conf. on support for education and research in Math. Sci., Delhi (1989).
• Venkataraman – a tribute, UGC Jour. Math. Edu., (1991).
• Hausdorff-Young Theorem, Math. Newsletter, 1991.
• Presidential Address (general), 58^th Annual Conf. of the Indian Math. Soc., BHU, Varanasi (1993).
• The language of Mathematics, AP Jour. Math. Research (1994).
• Profiles in scientific research contributions of fellows, Vol. I, Diamond Jubilee Publications, INSA, (1995) 49-55.
• Lessons learnt from Prof. M. Venkatraman, AP Jour. Math. Research (1999).
• Lagadha, In the book “Ancient Indian Mathematicians”, 2010, 1-10.

Edited Books

• Fractals, Wavelets and Geometry, Bernsley, V.Kannan , Springer Verlag 2015.
  Articles in subjects other than Mathematics. (About 200 articles in Sanskrit, Tamil and English in about ten magazines and journals). List not included here.