# Anna M. Vishnyakova

Professor of the department of pure mathematics, doctor of sciences in mathematics

**Education and Degrees**

M.Sc. in Math. (with Honours) – Kharkov State University, 1985.

Ph.D. in Math. – The Growth and Distribution of Zeros of Analytic Characteristic and Ridge Functions, Kharkov State University, 1993 (Supervisor – Prof. I.V.Ostrovskii, reviewers – Prof. V.S.Azarin and Prof. V.N.Logvinenko).

Doctor of Sci. in Math – Polynomials with Restrictions on the Location of Roots and the Limiting Classes of Entire Functions, 2019.

**Professional Career**

Assistant Professor – Kharkov State University, 1993.

Associate Professor – Kharkov National V.N. Karazin University, 1999.

Professor -- Kharkov National V.N. Karazin University, 2020.

**Research interests**

Complex analysis; special classes of entire functions: growth estimates and distribution of zeros; polynomials: location of zeros; total and multiple positivity

My profile in Google scholar:

https://scholar.google.com.ua/citations?hl=ru&user...

My profile in Researchgate:

https://www.researchgate.net/profile/Anna_Vishnyak...

**List of Publications**

All publications are available here:

https://www.researchgate.net/profile/Anna-Vishnyak...

1. I.V. Ostrovskii and A.M. Vishnyakova, Analogue of Marcinkiewicz' theorem for entire ridge functions not having zeros in an angular domain, Dokl. Akad. Nauk Ukr. SSR, ser. A, 1987, No.9, 8-11 (in Russian, English summary).

2. A.M. Vishnyakova, On the growth of ridge functions not having zeros in an angular domain, Analytic. Methods in the Probability Theory and in the Operator Theory, (ed. by V.A.Marchenko), Kiev, Naukova Dumka, 1990, 40-48 (in Russian).

3. I.V. Ostrovskii, A.M. Ulanovskii and A.M. Vishnyakova, On a conjecture of Yu.V.Linnik, Algebra i Analiz, 2 (1990), No 4, 82-90 (in Russian), English translation: Leningr. Math. J., 2, No. 4, 765-773 1991.

4. A.M. Vishnyakova, On the growth of functions, which are ridge in the half-plane, Operator theory, subharmonic functions, (ed. by V.A.Marchenko), Kiev, Naukova Dumka, 24-30, 1991 (in Russian).

5. A.M. Vishnyakova, Growth of entire ridge functions with restrictions on the arguments of zeros, Ukr. Mat. Zh., 43, No.6, 677-683, (1991) (in Russian), English translation: translation from Ukr. Mat. Zh., 43, No.6, 727-734 (1991).

6. A.M. Vishnyakova, On the growth of ridge functions non-vanishing in an angular domain, Bull. Hong Kong Math. Soc., 1, No.2, 351-361, 1997.

7. O.M. Katkova and A.M. Vishnyakova, A note on zero sets of absolutely monotonic functions, Vestnik of Kharkov Univ., ser. Matem., 49, 2000, No 475, 70-75.

8. Olga M. Katkova and Anna M. Vishnyakova, A continual analogue of a theorem by M. Fekete and G. Polya, Positivity, No 5, pp. 1-11, 2001.

9. E. Behrends and O. Katkova and A. Vishnyakova, A note on l^p-norms, Archiv der Mathematik, No 76, pp. 67-72, 2001.

10. O. Katkova and A. Vishnyakova, Zero sets of entire absolutely monotonic functions, Entire functions in modern analysis, Israel Mathematical Conference Proceedings, Vol. 15, pp. 173-205, 2001.

11. Olga M. Katkova, Tetyana Lobova and Anna M. Vishnyakova, On Power Series Having Sections with Only Real Zeros, Comput. Methods Funct. Theory, 2003 (3), No. 2, 425—441.

12. Olga M. Katkova and Anna M. Vishnyakova, On the zeros of entire absolutely monotonic functions, Journal of Mathematical Physics, Analysis, Geometry, Vol. 11, No 1, pp. 25 – 44, 2004.

13. Olga M. Katkova, Tatjana Lobova-Eisner and Anna M. Vishnyakova, On entire functions having Taylor sections with only real zeros, Journal of Mathematical Physics, Analysis, Geometry, Vol. 11, No 4, pp. 449 – 469, 2004.

14. Olga M. Katkova and Anna M. Vishnyakova, On sufficient conditions for the total positivity and for the multiple positivity of matrices, Linear Algebra and its Applications, 416, pp. 1083-1097, 2006.

15. Olga M. Katkova and Anna M. Vishnyakova, A sufficient condition for a polynomial to be stable, Journal of Mathematical Analysis and Applications, 347, pp. 81-89, 2008.

16. Vladimir Kadets, Olga Katkova, Miguel Martin and Anna Vishnyakova, Convexity around the unit of a Banach algebra, Serdica Math. J., 34, 619-628, 2008.

17. Olga M. Katkova and Anna M. Vishnyakova, On the stability of Taylor sections of a function $\sum_{k=0}^\infty \frac{z^k}{a^{k^2}}, \ a>1$, Comput. Methods Funct. Theory, 9, No. 1, 305—322, 2009.

18. Olga M. Katkova and Anna M. Vishnyakova, Linear operators preserving the set of positive (nonnegative) polynomials, Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 09) Valencia, Spain, September 2-4, 2009; Series: Lecture Notes in Control and Information Sciences , Vol. 389, 83-90 Bru, Rafael; Romero-Vivó, Sergio (Eds.), 2009, XII, 398 p. ( Zbl 1182.93061).

19. Olga M. Katkova and Anna M. Vishnyakova, A remark about positive polynomials, Mathematical Inequalities & Applications, 13, No. 4, 753-759, 2010. (https://www.scopus.com/record/display.uri?eid=2-s2.0- 78149309042&origin=inward&txGid=6b55aa00f35a079487cbc1af085c7713) .

20. Olga Katkova, Boris Shapiro and Anna Vishnyakova, Multiplier sequences and logarithmic mesh, Comptes rendus - Mathématique 349 (2011), pp. 35--38, DOI information: 10.1016/j.crma.2010.11.031 (https://www.scopus.com/record/display.uri?eid=2-s2.0-78651324942&origin=inward&txGid=e8b8c1ef80ed23f304630e274331e388).

21. George Csordas and Anna Vishnyakova, The generalized Laguerre inequalities and functions in the Laguerre-Pólya class, Cent. Eur. J. Math., 2013, 11(9), 1643--1650 DOI: 10.2478/s11533-013-0269-x (https://www.scopus.com/record/display.uri?eid=2-s2.0-84879703746&origin=inward&txGid=fec25a3f43ba7a2737f9ea8c5fe7d849).

22. Olga Katkova and Anna Vishnyakova, The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone, Cent. Eur. J. Math., May 2014, 12 (5), pp 752--760, DOI: 10.2478/s11533-013-0380-z (https://www.scopus.com/record/display.uri?eid=2-s2.0-84893948466&origin=inward&txGid=7f8fd4c67ddd8638b6c4f7d2eff2fba0).

23. Anton Bohdanov and Anna Vishnyakova, On the conditions for entire functions related to the partial theta function to belong to the Laguerre-P\'olya class, Journal of Mathematical Analysis and Applications, 434 (2), 15 February 2016, pp 1740–1752, doi:10.1016/j.jmaa.2015.09.084 (https://www.scopus.com/record/display.uri?eid=2-s2.0-84946430510&origin=inward&txGid=7a7df5054edbadb06205f86033db25a3).

24. Irina Karpenko and Anna Vishnyakova, On sufficient conditions for a polynomial to be sign-independently hyperbolic or to have real separated zeros, Mathematical Inequalities & Applications, 20 (1), 2017, pp 237–245. doi:10.7153/mia-20-18. (https://www.scopus.com/record/display.uri?eid=2-s2.0-85014724231&origin=inward&txGid=74a4503e09e777298caa1e8bd96e4c1f) .

25. Olga Katkova, Mikhail Tyaglov and Anna Vishnyakova, Linear finite difference operators preserving Laguerre-P\'olya class, Complex Variables and Elliptic Equations, Volume 63, 11, 2018, PP. 1604-1619 doi:10.1080/17476933.2017.1400539 https://www.scopus.com/record/display.uri?eid=2-s2... .

26. Thu Hien Nguyen and Anna Vishnyakova, On the entire functions from the Laguerre-P\'olya class having the decreasing second quotients of Taylor coefficients, Journal of Mathematical Analysis and Applications, 465 (1), 2018, pp 348–358, doi:10.1016/j.jmaa.2018.05.018. (https://www.scopus.com/record/display.uri?eid=2-s2.0-85047101932&origin=inward&txGid=f64b623c7e36a6ee4523e97ce153d1ea).

27. Thu Hien Nguyen and Anna Vishnyakova, On a necessary condition for an entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-P\'olya class, Journal of Mathematical Analysis and Applications, 480 (2), 2019, https://doi.org/10.1016/j.jmaa.2019.123433 .

28. Olga Katkova, Mikhail Tyaglov and Anna Vishnyakova, Hermite-Poulain theorems for linear finite difference operators, Constructive Approximation, 52 (3), 2020, pp. 357–393, https://doi.org/10.1007/s00365-020-09507-0 .

29. Thu Hien Nguyen and Anna Vishnyakova, On the Closest to Zero Roots and the Second Quotients of Taylor Coefficients of Entire Functions from the Laguerre–Polya I Class, Results in Mathematics, 75, 115 (2020). https://doi.org/10.1007/s00025-020-01245-w .

30. Thu Hien Nguyen and Anna Vishnyakova, On the entire functions from the Laguerre--Polya I class having the increasing second quotients of Taylor coefficients, Journal of Mathematical Analysis and Applications, 498, Issue 1, 1 June 2021,https://doi.org/10.1016/j.jmaa.2021.124955.

31. Thu Hien Nguyen and Anna Vishnyakova, On the entire functions from the Laguerre-Polya I class with non-monotonic second quotients of Taylor coefficients, “Matematychni Studii”, 56, No. 2, 2021, p. 149-162.

DOI: https://doi.org/10.30970/ms.56.2.149-161

32. Thu Hien Nguyen and Anna Vishnyakova, On the number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients, Mathematical Inequalities and Applications, 25, No. 1 (2022), 73–89. DOI: https://dx.doi.org/10.7153/mia-2022-25-06.

33. Kateryna Bielenova, Hryhoriy Nazarenko and Anna Vishnyakova, A sufficient condition for a complex polynomial to have only simple zeros and an analog of Hutchinson's theorem for real polynomials, Mathematical Inequalities & Applications, 26, No. 1 (2023), 69–82. doi:10.7153/mia-2023-26-06.

34. Thu Hien Nguyen and Anna Vishnyakova, Hutchinson's intervals & the Laguerre--Polya class, European Journal of Mathematics, 10 (2024) DOI: https://doi.org/10.1007/s40879-023-00723-z

35. L. Golinskii, S. Kupin, and A. Vishnyakova, On the growth of resolvent of Toeplitz Operators, arXiv:2401.12095v1 [math.SP] 22 Jan 2024.

36. Olga Katkova, Boris Shapiro, and Anna Vishnyakova, In search of Newton-type inequalities, Journal of Mathematical Analysis and Applications, Volume 538, Issue 1, 1 October 2024, article No. 128349, DOI: https://doi.org/10.1016/j.jmaa.2024.128349.

37. Olga Katkova and Anna Vishnyakova, An analog of multiplier sequences for the set of totally positive sequences, arXiv:2402.05017.

38. Anna Vishnyakova and Olesia Zavarzina, Linear algebra, Tutorial book, Kharkiv National V.N. Karazin University, Kharkiv, 2024, 160 p. (in Ukrainian), https://ekhnuir.karazin.ua/items/da3d7c04-932b-41...

**International Collaboration**

**Visiting Scientist**:

– American Institute of Mathematics, Palo Alto, California, USA (2007);

– University of Ankara, Ankara, Turkey (2009);

– Stockholm University, Stockholm, Sweden (2010),

– American Institute of Mathematics, Palo Alto, California, USA (2011);

– Stockholm University, Stockholm, Sweden (2012);

– University of Leipzig, Leipzig, Germany (2014);

– Shanghai Jiao Tong University, Shanghai, China (April-May 2015);

– Shanghai Jiao Tong University, Shanghai, China (July 2015);

– University of Leipzig, Leipzig, Germany (2018).

**Mathematical Conferences **(since 2000)

1. Computational Methods and Function Theory, International Conference, June 25-29, 2001, University of Aveiro, Portugal, 2001.

2. International Akhiezer Centenary Conference “Theory of Functions and Mathematical Phisics”, International Conference, August 13-17, 2001, Kharkiv, Ukraine.

3. Second International Conference “Mathematical Analysis and Economics”, International Conference, April 1-4, 2003, Sumy, Ukraine.

4. International conference dedicated to 125-th anniversary of Hans Hahn, International Conference, June 27 - July 3, 2004, Chernivtsi, Ukraine.

5. Computational Methods and Function Theory, International Conference, June 13-17, 2005, Joensuu, Finland.

6. Analysis and related topics, International Conference, November 17-20, 2005, Lviv, Ukraine.

7. Entire and Subharmonic Functions and Related Topics, International Conference dedicated to the centennial of B.Ya.Levin (1906-1993), International Conference, August 14-17, 2006, Kharkiv, Ukraine.

8. Analysis and Topology, International Conference, May 26-June 7, 2008, Lviv, Ukraine.

9. Conference on complex analysis dedicated to the memory of Anatolii Asirovich Goldberg (1930-2008), International Conference, May 31-June 5, 2010, Lviv, Ukraine.

10. IWOTA 2010, International Conference, July 12-16, 2010, Technische Universitat Berlin, Germany.

11. Complex analysis and its applications, dedicated to the 70th anniversary of A.F. Grishin, International Conference, August 15-18, 2011, Kharkov National University, Ukraine.

12. III International Conference ANALYSIS AND MATHEMATICAL PHYSICS, International Conference, June 15–19, 2015, B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine.

13. Complex Analysis and Related Topics, International Conference, May 30-June 4, 2016, Ivan Franko National University of Lviv, Lviv, Ukraine.

14. International Conference in Functional Analysis Dedicated to the 125th Anniversary of Stefan Banach, International Conference, September 18-23, 2017, Ivan Franko National University of Lviv, Lviv, Ukraine.

15. Hausdorff Geometry of Polynomials and Polynomial Sequences, International Conference, May 28 - June 1, 2018, Institut Mittag-Leffler, Sweeden.

16. VI International Conference ANALYSIS AND MATHEMATICAL PHYSICS dedicated to the centennial anniversary of the National Academy of Sciences of Ukraine and the 50th anniversary of the Department of Function Theory, International Conference, June 18–22, 2018, B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine.

17**. **Ukrainian Conference "Modern Problems of Probability Theory and Mathematical Analysis", Vorokhta, February 26 - March 01, 2020.

18.The International Conference ``Computational Methods and Functional Theory'', Stephan Ruscheweyh, in memoriam, January 10-14, 2022, Virtual Conference, Valparaiso, Chile.

19. The International Conference “The Laguerre-Polya Class and Combinatorics”, Oberwolfach, Germany, March 13-19, 2022.

20. The International Conference ``Harmonic and Complex Analysis: modern and classical'', June 18--23, 2023, Bar-Ilan University, Israel.

21. Workshop on: Theory and applications of total positivity, July 24-28, 2023, AIM, Pasadena, CA, USA.

**Courses and seminars given within last 5 years**

Linear Algebra, General Algebra, Complex Analysis, Functional Analysis, Measure Theory, Meromorphic Functions, Constructive Function Theory, Distribution of Zeros of Polynomials

**E-mail**: anna.vishnyakova@karazin.ua

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