Publications and Research Funding

Selected Recent Publications

Aldroubi, C. Cabrelli, I. Krishtal, and U. Molter. Dynamical sampling: A survey. La Matematica 5, Article 37 (2026).

Krishtal, J. Mashreghi, and B. Miller. Frames from functional calculus. Sampling Theory, Signal Processing, and Data Analysis 24, Article 8 (2026).

Krishtal and B. Miller. Demystifying Carleson frames. Appl. Comput. Harmon. Anal. 80, Article 101811 (2026).

Aldroubi, L. Gong, I. Krishtal, B. Miller, and S. Thareja. Reconstruction algorithms for source term recovery from dynamical samples in catalyst models. J. Fourier Anal. Appl. 31, no. 4, Article 53 (2025).

Krishtal and B. Miller. Kadec-type theorems for sampled group orbits. Appl. Comput. Harmon. Anal. 76, Article 101748 (2025).

A. Krishtal and G. E. Pfander. Prony’s method in Banach modules. J. Fourier Anal. Appl. 31, no. 6, Article 72 (2025).

Aldroubi, L. Gong, and I. Krishtal. Recovery of rapidly decaying source terms from dynamical samples in evolution equations. Sampl. Theory Signal Process. Data Anal. 21, no. 1, Article 15 (2023).

Aldroubi, L. Huang, K. Kornelson, and I. Krishtal. Predictive algorithms in dynamical sampling for burst-like forcing terms. Appl. Comput. Harmon. Anal. 65 (2023), pp. 322–347.

G. Baskakov, I. A. Krishtal, and N. B. Uskova. Method of similar operators in the study of spectral properties of perturbed first-order differential operators. J. Math. Sci., New York 263, no. 5 (2022), pp. 599–615. Russian original: Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz. 171 (2019), 3–18.

G. Baskakov, G. V. Garkavenko, I. A. Krishtal, and N. B. Uskova. Method of similar operators in the problem of bi-invariant subspaces. Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz. 204 (2022), pp. 3–15.

G. Baskakov, I. A. Krishtal, and N. B. Uskova. On smoothing the operator coefficient of a first-order differential operator in a Banach space. Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz. 206 (2022), pp. 3–14.

Aldroubi, K. Gröchenig, L. Huang, P. Jaming, I. Krishtal, and J. L. Romero. Sampling the flow of a bandlimited function. J. Geom. Anal. 31, no. 9 (2021), pp. 9241–9275.

G. Baskakov, I. A. Krishtal, and N. B. Uskova. Spectral properties of classical Dirac operators and operators with involution in homogeneous function spaces. Differ. Equ. 57, no. 10 (2021), pp. 1273–1278.

G. Baskakov, I. A. Krishtal, and N. B. Uskova. Spectral properties of the Dirac operator on the real line. Differ. Equ. 57, no. 2 (2021), pp. 139–147.

G. Baskakov, G. V. Garkavenko, I. A. Krishtal, and N. B. Uskova. The method of similar operators in the spectral analysis of infinite operator matrices. Examples II. Applied Mathematics & Physics 53, no. 3 (2021), pp. 205–212.

G. Baskakov and I. A. Krishtal. A primer on the spectral theory of Banach modules and a few of its applications. Science ONLINE no. 1 (14) (2021), pp. 94–100.

Published Book Chapters

Krishtal and B. Miller. On low-rank convex-convex quadratic fractional programming. In: The Mathematical Heritage of Guido Weiss. Applied and Numerical Harmonic Analysis. Cham: Birkhäuser, 2025, pp. 331–345.

G. Baskakov and I. A. Krishtal. Spectral properties of an operator polynomial with coefficients in a Banach algebra. In: Frames and Harmonic Analysis. Vol. 706. Contemporary Mathematics. Providence, RI: American Mathematical Society, 2018, pp. 93–114.

Aldroubi, I. Krishtal, and E. Weber. Finite dimensional dynamical sampling: an overview. In: Excursions in Harmonic Analysis. Vol. 4. Cham: Birkhäuser, 2015, pp. 231–244.

More Publications

Curriculum Vitae (DOCX) 

Research Funding

2022–2025 NSF, Computational Mathematics, $182,637. Co-PI, “Collaborative Research: Dynamical Sampling on Graphs: Mathematical Framework and Algorithms.”

2013–2019 NSF, Algorithms for Threat Detection, $272,112. Co-PI, “Collaborative Research: ATD: Dynamical Sampling and Reconstruction for Sensing Networks of Physical Fields.”

2009–2012 NSF, Applied Mathematics, $99,936. PI, “Matrix-like Representations in Time Frequency and Applied Harmonic Analysis.”