Welcome to the web page of Ilya Krishtal!  

I am a mathematician, and currently work as an
Associate Professor
at the Department of Mathematical Sciences at
Northern Illinois University

Contact information:
e-mail: krishtal @ math.niu.edu
phone: (815)-753-6769
fax:      (815)-753-1112

Address:  Ilya Krishtal   
Department of Mathematics
Northern Illinois University
DeKalb, IL 60115, USA

 brief resumepublications, courses, IMAHA VII, picture gallery.


  1. A. Aldroubi, J. Davis, IK. Dynamical sampling: time-space trade-off, Appl. Comput. Harmon. Anal., Volume 34, Issue 3, May 2013, Pages 495-503, 2012doi
  2. A. Aldroubi, IK, R. Tessera, and H. Wang. Principal shift-invariant spaces with extra invariance nearest to observed data, Collect. Math., Vol. 63, no. 3, 2012, pp. 393-401, doi, pdf.
  3. J. Blanchard and IK. Matricial Filters for Crystallographic Composite Dilation Wavelets, Math. Comp., Volume 81, no. 278, 2012, pp. 905-922, doi, pdf.
  4. IK. Wiener's Lemma: Pictures at an exhibition, Rev. Un. Mat. Argentina, Volume 52, no. 2, 2011, pp. 61-79, pdf.
  5. IK. Wiener's Lemma and memory localization, J. Fourier Anal. Appl., Volume 17, no. 4, 2011, pp. 674-690, doi, pdf.
  6. R. Balan and IK. An almost periodic noncommutative Wiener's lemma, J. Math. Anal. Appl., Volume 370, Issue 2, 2010, pp. 339-349, doi, pdf.
  7. E. Acosta-Reyes, A. Aldroubi, and IK. On stability of sampling-reconstruction models, Adv. Comp. Math., Vol. 31, 2009, pp. 5-34, doi, pdf.
  8. A. Aldroubi, A.G. Baskakov, and IK. Slanted matrices, Banach frames, and sampling, J. Funct. Anal., Vol. 255/7,  2008, pp. 1667-1691, doi, pdf
  9. IK and K. Okoudjou. Invertibility of the Gabor frame operator on the Wiener amalgam space, J. Approx. Theory, Vol. 153/2, 2008, pp.212-224, doi, pdf
  10. A. Aldroubi, A.G. Baskakov, and IK. On slanted matrices in frames theory, in Proceedings of SPIE "Wavelets XII", 6701 0Q, 2007, pdf
  11. IK, B. Robinson, G. Weiss, and E. Wilson. Some simple Haar–type wavelets in higher dimensions, J. Geom. Anal., Vol. 17/1, 2007, pp. 87-96, pdf
  12. A. Aldroubi and IK. Robustness of sampling and reconstruction and Beurling-Landau type thorems for shift invariant spaces, Appl. Comput. Harmon. Anal., Vol 20/2, 2006, pp. 250-260, doi, dvi, ps.
  13. A.G. Baskakov and IK. On harmonic analysis of causal operators,  Functional Analysis and Its Applications, Vol. 40/1, 2006, pp. 52-55, doi, pdf
  14. D. Bakic, IK, and E. Wilson. Parseval frame wavelets with En(2)-dilations, Appl. Comput. Harmon. Anal., Vol. 19/3, 2005, pp. 386-431, doi, dvi, ps.
  15. A.G. Baskakov and IK. Harmonic analysis of causal operators and their spectral properties, Izvestiya: Mathematics  3 (69) 2005, pp. 439-486, doi, ps (Russian, preliminary), pdf (English).
  16. A.G. Baskakov and IK. Spectral analysis of operators with the two-point Bohr spectrum, J. Math. Anal. Appl., Volume 308, Issue 2, 2005, pp. 420-439, doi.


  1. A.G. Baskakov and IK. On harmonic analysis of causal operators and their spectral properties, Tübinger berichter, 2003, preprint.
  2. A.G. Baskakov and IK. On the spectral properties of causal operators, Vestnik VGU: Physics, Mathematics, No. 2, 2002, pdf (Russian), description.
  3. IK. On invertibility criteria in the algebra of causal operators, Vestnik VGU: Physics, Mathematics, No. 1, 2002, pdf (Russian), description.
  4. IK. Different banach module spectra as a key to the spectral mapping theorem, Proceedings of the V TULKA Internet Seminar, Karlsruhe, 2002.
  5. IK. Invertibility and causal invertibility of operators with the two-point Beurling spectrum, Izvestiya Ross. Akad. Estestv. Nauk, Ser. MMMIU, 4 (4), 2000, description.
  6. S.Yu. Balasheva, IK, I.A. Rodionova, and N.A. Zhdankina. On a problem of uniform distribution of multiplying traffic flows, In "System modeling of socio-economic processes," Voronezh, 2000, pp. 47-51, (Russian), description.
  7. IK and T. Vinokurova. Preference projection method for a neoclassic consumption model, In "System modeling of socio-economic processes," Voronezh, 2000, pp. 72-74, (Russian), description.
  8. I.F. Astakhova, IK et al. Employment of expert system generator "Expert-M" when working with economic models, Interuniversitary collection of articles "Russian Eonomy at Present," Voronezh, 1998, pp. 18-28, (Russian), description.
  9. I.F. Astakhova and IK. Expert system generator "Expert-M" , Student manual, Voronezh, 1998, 20 p., (Russian), description.
  10. IK. On C*-algebras generated by one or two idempotents, Vestnik VGU: Physics, Mathematics, No. 3, 1998, description.


  • TGU Lecture series, Togliatti State University, Russia, December 15-18, 2009, pdf1, pdf2.
  • Fall Southeastern AMS Meetintg, Boca Raton, FL, October 31, 2009.
  • Wavelet Seminar, Washington University in St. Louis, September 25, 2009.
  • The international conference WAVELETS AND APPLICATIONS, St. Petersburg, Russia, June 15, 2009, pdf .
  • AMS Spring Central Sectional Meeting, Urbana, IL, March 28, 2009.
  • IWOTA 2008, Williamsburg, VA, July 26, 2008, pdf .
  • Analysis Seminar, Ben Gurion University of the Negev, Beer Sheva, Israel, June 16, 2008.
  • Applied Math Seminar, University of Utah, Salt Lake City, March 31, 2008, pdf .
  • Wavelets and frames, Zagreb, Croatia, March 13, 2008.
  • 24th SEAM, Nashville,TN, March 7, 2008.
  • SPIE Optics+Photonics, Wavelets XII, San Diego, CA, August 27, 2007, pdf.
  • Trends in Harmonic Analysis, Strobl, Austria, June 18, 2007, pdf.
  • IMA Short Course on Compressed Sensing, Minneapolis, MN, June 14, 2007, pdf.
  • Illinois Applied Harmonic Analysis Seminar, Urbana-Champaign, IL, December 2, 2006, pdf.


    CURRENT SYLLABI - see Blackboard 


    At Northern Illinois University:

    Math 229 Calculus I (S,Su,F'07),
    Math 430 Advanced Calculus (S,F'07),
    Math 336 Differential Equations (F'06)

    In Washington University in St. Louis (F2003-S2006):

    Math 141 Accelerated Calculus I
    Math 142 Accelerated Calculus II
    Math 217 Differential Equations
    Math 233 Calculus III
    Math 410   Introduction to Fourier Series and Integrals
    Math 4111 Introduction to Analysis
    Math 4121 Introduction to Lebesgue Integration