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College of Science and Mathematics

Marat Markin

Associate Professor

Mathematics | 559-278-1078 | Office: PB 353

mmarkin@csufresno.edu

Education

M.S. Mathematics, Kiev State University, Ukraine
Ph.D. Physico-Mathematical Sciences, Institute of Mathematics, National Academy of Sciences of Ukraine


Office Hours (Spring 2025)

3:55 pm - 5:25 pm (in person) & 6:55 pm - 7:55 pm (via Zoom)

Courses Taught

Current Courses (Spring 2025)

MATH 70
MATH 81
MATH 171


Previous Courses

MATH 1RA
MATH 1RB
MATH 6
MATH 70
MATH 75A
MATH 75B
MATH 76
MATH 81
MATH 152
MATH 181
MATH 190
MATH 198
MATH 223
MATH 228
MATH 263
MATH 271
MATH 272
MATH 290
MATH 291T
MATH 298
MATH 299
  • Associate Professor — Department of Mathematics, California State University, Fresno (August 2020 – present)
  • Assistant Professor — Department of Mathematics, California State University, Fresno (August 2016 – August 2020)
  • Part-Time Lecturer — Department of Mathematics, California State University, Fresno (January 2013 – August 2016)
  • Supernumerary Research Fellow — Department of Partial Differential Equations, Institute of Mathematics, National Academy of Sciences of Ukraine (September 2002 – December 2012)
  • Assistant Professor—Department of Mathematics and Statistics, Boston University (Academic Year 2001 – 2002)
  • Assistant Professor — Division of Science and Mathematics, College of General Studies, Boston University (Academic Year 2000 – 2001)
  • Visiting Assistant Professor — Department of Mathematics, University of North Carolina, Asheville (Fall 1999 – Summer 2000)
  • Adjunct Assistant Professor — Department of Mathematics, University of North Carolina, Asheville (Fall 1997 – Summer 1999)
  • Adjunct Professor — Department of Mathematics, Warren Wilson College (Spring 1998)
  • Mathematics Instructor — Upward Bound Mathematics and Science Regional Center, Western Carolina University (Summer 1997)
  • Part-Time Assistant Professor—Department of Higher Mathematics, National University of Food Technologies, Kiev, Ukraine (Spring 1994, Academic Years 1994 – 1995, 1995 – 1996)
  • Junior Research Fellow — Department of Partial Differential Equations, Institute of Mathematics, National Academy of Sciences of Ukraine (January 1995 – October 1996)
Functional Analysis
Operator Theory
Differential Equations in Abstract Spaces
Semigroups of Operators
Linear Chaos and Hypercyclicity 
Peer Reviewed Papers
  1. On linear chaos in function spaces, Demonstr. Math. 55 (2022), no. 1, 119–135. (co-authored with John M. Jimenez)
  2. On a characterization of convergence in Banach spaces with a Schauder basis, Int. J. Math. Math. Sci. 2021 (2021), Article ID 1640183, 5 pp. (co-authored with Olivia B. Soghomonian)
  3. On a characterization of finite-dimensional vector spaces, Int. J. Math. Math. Sci. 2021 (2021), Article ID 8895949, 3 pp.
  4. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis, Open Math. 18 (2020), no. 1, 1952–1976.
  5. On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials, Demonstr. Math. 53 (2020), no. 1, 352–359.
  6. On expansive mappings, Mathematics 7 (2019), no. 11, Article no. 1004, 10 pp. (coauthored with Edward S. Sichel)
  7. On the non-hypercyclicity of normal operators, their exponentials, and symmetric operators, Mathematics 7 (2019), no. 10, Article no. 903, 8 pp. (co-authored with Edward S. Sichel)
  8. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis, Open Math. 17 (2019), no. 1, 1082–1112.
  9. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one, Open Math. 17 (2019), no. 1, 1–14.
  10. On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator, Methods Funct. Anal. Topology 24 (2018), no. 4, 349–369.
  11. On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis, Int. J. Math. Math. Sci. 2018 (2018), Article ID 4168609, 14 pp.
  12. On the mean ergodicity of weak solutions of an abstract evolution equation, Methods Funct. Anal. Topology 24 (2018), no. 1, 53–70.
  13. Comment on “On the Carleman classes of vectors of a scalar type spectral operator”, Int. J. Math. Math. Sci. 2018 (2018), Article ID 2135740, 3 pp.
  14. On certain spectral features inherent to scalar type spectral operators, Methods Funct. Anal. Topology 23 (2017), no. 1, 60–65.
  15. On the generation of Beurling type Carleman ultradifferentiable C_0-semigroups by scalar type spectral operators, Methods Funct. Anal. Topology 22 (2016), no. 2, 169–183.
  16. On the Carleman ultradifferentiable vectors of a scalar type spectral operator, Methods Funct. Anal. Topology 21 (2015), no. 4, 361–369.
  17. On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator, Int. J. Math. Math. Sci. 2011 (2011), Article ID 825951, 27 pp.
  18. On the Carleman ultradifferentiability of weak solutions of an abstract evolution equation, Modern Analysis and Applications. The Mark Krein Centenary Conference. Vol. 2: Differential Operators and Mechanics, 407–443, Oper. Theory Adv. Appl., vol. 191, Birkh¨auser Verlag, Basel, 2009.
  19. On scalar type spectral operators and Carleman ultradifferentiable C_0-semigroups, Ukrainian Math. J. 60 (2008), no. 9, 1418–1436.
  20. A note on one decomposition of Banach spaces, Methods Funct. Anal. Topology 12 (2006), no. 3, 254–257.
  21. A Gelfand-Mazur type theorem for normed algebras, Methods Funct. Anal. Topology 11 (2005), no. 1, 63–64.
  22. A characterization of the generators of analytic C_0-semigroups in the class of scalar type spectral operators, Abstr. Appl. Anal. 2004 (2004), no. 12, 1007–1018.
  23. On the Carleman classes of vectors of a scalar type spectral operator, Int. J. Math. Math. Sci. 2004 (2004), no. 60, 3219–3235.
  24. On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable C_0-semigroups, Int. J. Math. Math. Sci. 2004 (2004), no. 45, 2401–2422.
  25. A note on the spectral operators of scalar type and semigroups of bounded linear operators, Int. J. Math. Math. Sci. 32 (2002), no. 10, 635–640.
  26. On an abstract evolution equation with a spectral operator of scalar type, Int. J. Math. Math. Sci. 32 (2002), no. 9, 555–563.
  27. On the strong smoothness of weak solutions of an abstract evolution equation. III. Gevrey ultradifferentiability of orders less than one, Appl. Anal. 78 (2001), no. 1-2, 139–152.
  28. On the strong smoothness of weak solutions of an abstract evolution equation. II. Gevrey ultradifferentiability, Appl. Anal. 78 (2001), no. 1-2, 97–137.
  29. On the strong smoothness of weak solutions of an abstract evolution equation. I. Differentiability, Appl. Anal. 73 (1999), no. 3-4, 573–606.
  30. On a characterization of the generators of the analytic semigroups in the class of normal operators, Methods Funct. Anal. Topology 2 (1996), no. 2, 86–93.
  31. On the ultradifferentiability of weak solutions of a first-order operator-differential equation in Hilbert space, Dopov. Nats. Akad. Nauk Ukra¨ıni 1996, no. 6, 22–26.
  32. On the smoothness of weak solutions of a first-order differential equation in a Hilbert space, Dopov./Dokl. Akad. Nauk Ukra¨ıni 1994, no. 4, 23–25.
  33. Ergodicity of weak solutions of a first-order operator-differential equation, Akad. Nauk Ukrainy, Inst. Mat., Preprint 1994, no. 10, 44 pp.
  34. On the behavior at infinity of bounded solutions of differential equations in a Banach space, Boundary Value Problems for Operator-Differential Equations, 56–63, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1991 (Russian).
  35. On the strong continuity of functions defined on a compact set with values in a Banach space with a basis, Mathematics Today ’90, no. 6, 110–118, Vishcha Shkola, Kiev, 1990 (Russian).
Books Authored
  1. Elementary Operator Theory, De Gruyter Graduate, Walter de Gruyter GmbH, Berlin/Boston, 2020.
  2. Real Analysis. Measure and Integration, De Gruyter Graduate, Walter de Gruyter GmbH, Berlin/Boston, 2019.
  3. Elementary Functional Analysis, De Gruyter Graduate, Walter de Gruyter GmbH, Berlin/Boston, 2018.
  4. Integration for Calculus, Analysis, and Differential Equations: Techniques, Examples, and Exercises, World Scientific Publishing Co. Pte. Ltd., New Jersey-London-Singapore, 2019.
Books Co-Edited
  1. Advances in Functional Analysis and Operator Theory, AMS-EMS-SMF Special Session, Universit´e de Grenoble-Alpes, Grenoble, France, July 18-22, 2022, Contemporary Mathematics, vol. 798, American Mathematical Society, Providence, RI, 2024. (co-edited with Igor V. Nikolaev and Carsten Trunk)
Preprints
  1. On hypercyclicity and linear chaos in a nonclassical sequence space and beyond, arXiv:2209.04515 (co-authored with Eric Montoya).
  2. On linear chaos in the space of convergent sequences, arXiv:2203.02032 (co-authored with Gabriel Martinez Lazaro and Edward S. Sichel).
  3. An observation on unbounded linear operators with an arbitrary spectrum, arXiv:2107.09638.
  4. On asymptotics for C_0-semigroups, arXiv:2107.02832.
  5. On sufficient and necessary conditions for linear hypercyclicity and chaos, arXiv:2106.14872.
  6. On the chaoticity of derivatives, arXiv:2106.09682.
  7. On the regularity of scalar type spectral C0-semigroups, arXiv:2103.05260.
  8. On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups, arXiv:2002.09087.
  9. On linear chaos in function spaces, arXiv:1912.03402 (co-authored with John M. Jimenez).
  10. On general construct of chaotic unbounded linear operators in Banach spaces with Schauder bases, arXiv:1812.02294.
  11. On the chaoticity and spectral structure of Rolewicz-type unbounded operators, arXiv:1811.06640.
Unpublished Manuscripts
  1. Elementary Differential Equations and Linear Algebra (a textbook co-authored with Doreen De Leon, used for teaching Elementary Differential Equations with Linear Algebra (MATH 81) course, in progress).
  2. Linear Algebra, Lecture Notes for MATH 152, CSU, Fresno, Spring 2022.
  3. Applied Operator Theory, Lecture Notes for MATH 223, CSU, Fresno, Spring 2019.
  4. Selected Topics in Functional Analysis, Lecture Notes for MATH 291T, CSU, Fresno, Spring 2018.
  5. Real Analysis, Lecture Notes for MATH 271, CSU, Fresno, Fall 2017.
  6. Applied Operator Theory, Lecture Notes for MATH 223, CSU, Fresno, Spring 2017.
  7. Point Set Topology, Lecture Notes for MATH 263, CSU, Fresno, Fall 2016.
  8. Introductory Functional Analysis, Lecture Notes for MATH 291T, CSU, Fresno, Spring 2016.
  9. Calculus II, Lecture Notes for MATH 76, CSU, Fresno, Spring 2016.
  10. Functions of a Complex Variable, Lecture Notes for MATH 228, CSU, Fresno, Spring 2015.
  11. Applied Analysis, Lecture Notes for MATH 81, CSU, Fresno, Spring 2014.
  12. Differential Equations, Lecture Notes for MATH 181, CSU, Fresno, Fall 2013.
  13. The Smoothness and Ergodicity of Weak Solutions of a First-Order Operator-Differential Equation, Ph.D. Thesis, Institute of Mathematics National Academy of Sciences of Ukraine, Kiev, 1994 (Ukrainian).
  14. Certain Issues of the Continuity of Vector Functions and the Theory of Semigroups of Operators, Master Thesis, Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Kiev State University, 1990 (Russian).
  15. On the Strong and Weak Continuity of Functions Defined on a Compact Set with Values in a Banach Space with a Basis, Term Paper, Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Kiev State University, 1989 (Russian).
  16. On the Strong Continuity of Functions Defined on a Compact Set with Values in a Banach Space with a Basis, Term Paper, Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Kiev State University, 1988 (Russian).
  17. Criteria of the Strong Continuity of Functions with Values in Certain Banach Spaces, Contribution to All-Ukrainian Contest of Student Research Works, Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Kiev State University, 1987 (Russian).
Grants
  1. National Science Foundation (NSF) Bridge to Doctorate Grant, Project: LSAMP BD: California State University, Fresno, CSU-LSAMP-BD Cohort 16; Award Number: 1905148; Award Amount: $1,075,000.00 (January 15, 2020 – December 31, 2021); Co-Principal Investigator.
  2. National Science Foundation (NSF) Travel Grant for U.S. Based Mathematicians to present at the 29th International Workshop on Operator Theory and Applications (IWOTA 2018), East China Normal University, Shanghai, China (July 23–27, 2018).
  3. National Science Foundation (NSF) Widening Implementation and Demonstration of Evidence-Based Reforms (WIDER) Grant for redesigning gateway Biology, Chemistry, Physics, and Mathematics major courses; Member for Academic Years 2016 – 2017, 2015 – 2016, 2014 – 2015.
  4. Ukrainian State Committee on Science and Technologies Research Grant 1(1)-3/30 (1992 – 1996).