• Department of Mathematics, Macquarie University

    Adam Sikora

    Research Interests

    Linear Partial Differential Equations and Harmonic Analysis, Analysis, Lie groups: singular integrals, spectral and Fourier multiplier theorems, Bochner-Riesz summability, functional calculi and spectral analysis of elliptic and sub-elliptic differential operators, spectral analysis of operators with periodic or almost periodic coefficients, Riesz transforms, semi-groups of operators and heat kernels, wave equation.

    Research Output

    "Si vous me savez peu de gré de ce que je vous dis, sachez m'en beaucoup de ce que je ne vous dis pas."
    Diderot Jacques le fataliste

  • Waldemar Hebisch and Adam Sikora
    A smooth subadditive homogeneous norm on a homogeneous group.
    Studia Math. 96 (1990), no. 3, 231-236.

  • Adam Sikora
    Multiplicateurs associés aux souslaplaciens sur les groupes homogènes. (French)
    [Multiplier theorem for sub-Laplacians on homogeneous groups]

    C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 4, 417-419.
    ps, dvi, pdf.

  • Adam Sikora
    Metoda rownania fali w badaniu eliptycznych i podeliptycznych operatorow rozniczkowych drugiego rzedu. (Polish)
    [The method of wave equation in investigation of elliptic and sub-elliptic second-order differential operators]

    Ph.D. Thesis, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland (1994).
    dvi, pdf.

  • Adam Sikora
    Sharp pointwise estimates on heat kernels.
    Quart. J. Math. Oxford Ser. (2) 47 (1996), no. 187, 371-382.
    dvi, pdf.

  • Adam Sikora
    On-diagonal estimates on Schrödinger semigroup kernels and reduced heat kernels.
    Comm. Math. Phys. 188 (1997), no. 1, 233-249.

  • A.F.M. ter Elst, Derek W. Robinson and Adam Sikora
    Heat kernels and Riesz transforms on nilpotent Lie groups.
    Colloq. Math. 74 (1997), no. 2, 191-218.

  • A.F.M. ter Elst, Derek W. Robinson and Adam Sikora
    Riesz transforms and Lie groups of polynomial growth.
    J. Funct. Anal. 162 (1999), no 1, 14-51.
    dvi, pdf.

  • Adam Sikora
    On the $L\sp 2\to L\sp \infty$ norms of spectral multipliers of "quasi-homogeneous" operators on homogeneous group.
    Trans. Amer. Math. Soc. 351 (1999), no 9, 3743-3755.
    dvi, pdf.

  • Nick Dungey, A.F.M ter Elst, Derek W. Robinson and Adam Sikora
    Asymptotics of subcoercive semigroups on nilpotent Lie groups.
    J. Operator Theory 45 (2001), no. 1, 81-110.

  • A.F.M. ter Elst, Derek W. Robinson and Adam Sikora
    On second-order periodic elliptic operators in divergence form.
    Math. Z. 238 (2001), no. 3, 569-637.
    dvi, pdf.

  • Adam Sikora and James Wright
    Imaginary powers of Laplace operators.
    Proc. Amer. Math. Soc. 129 (2001), no. 6, 1745-1754
    dvi, pdf.

  • Michael Cowling and Adam Sikora
    A spectral multiplier theorem for a sublaplacian on SU(2).
    Math. Z. 238 (2001), no. 1, 1-36.
    dvi, pdf.

  • Xuan Thinh Duong, El Maati Ouhabaz and Adam Sikora
    Plancherel type estimates and sharp spectral multipliers.
    J. Funct. Anal. 196 (2002), no. 2, 443-485.
    dvi, pdf.

  • Adam Sikora and Jacek Zienkiewicz
    A note on the heat kernel on the Heisenberg group.
    Bull. Austral. Math. Soc. 65 (2002), no. 1, 115-120.
    dvi, pdf.

  • Adam Sikora and Terence Tao
    Bochner-Riesz summability for analytic functions on the $m$-complex unit sphere and for cylindrically symmetric functions on $\R^{n-1} \times \R$.
    Comm. Anal. Geom. 12 (2004), no. 1-2, 43-57.
    (dvi, pdf, ps) arXiv: math.CA/0207225

  • Adam Sikora
    Riesz transform, Gaussian bounds and the method of wave equation.
    Math. Z. 247 (2004), no. 3, 643-662.
    (dvi, pdf, ps) arXiv: math.AP/0307291

  • A. F. M. ter Elst, Derek W. Robinson, Adam Sikora and Yueping Zhu
    Second-order operators with degenerate coefficients.
    Proc. London Math. Soc. To appear.
    (dvi, pdf, ps) arXiv: math.AP/0601307

  • A. F. M. ter Elst, Derek W. Robinson, Adam Sikora and Yueping Zhu
    Dirichlet forms and degenerate elliptic operators.
    Partial Differential Equations and Functional Analysis. Birkhauser.
    Philippe Clement Festschrift.
    Operator Theory: Advances and Applications, vol. 168 (2006), 73--95.
    (dvi, pdf, ps) arXiv: math.AP/0601349

  • A. F. M. ter Elst, Derek W. Robinson and Adam Sikora
    Small time asymptotics of diffusion processes.
    J. Evol. Equ. To appear.
    (dvi, pdf, ps) arXiv: math.AP/0601350

  • Derek W. Robinson and Adam Sikora
    Degenerate elliptic operators: capacity, flux and separation.
    (dvi, pdf, ps) arXiv: math.AP/0601350

  • Raphael J. Lyman and Adam Sikora
    Prediction of fading envelopes with diffuse spectra.
    Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, March (2005) vol. 3, III-753--III-756

  • Raphael J. Lyman and Adam Sikora
    Prediction of bandlimited fading envelopes with arbitrary spectral shape.
    IEEE Transactions on Wireless Communications

  • Derek W. Robinson and Adam Sikora
    Analysis of degenerate elliptic operators of Grushin type.
    (dvi, pdf, ps) arXiv: math.AP/0607584

  • Donggao Deng, Xuan Thinh Duong, Adam Sikora and Lixin Yan
    Comparison of the classical BMO with the BMO spaces associated with operators and applications.
    (dvi, pdf, ps) arXiv: math.AP/0609454

  • Thierry Coulhon and Adam Sikora
    Gaussian heat kernel upper bounds via Phragm\'en-Lindel\"of theorem.
    (dvi, pdf, ps) arXiv: math.AP/0609429

  • Andrew Hassell and Adam Sikora
    Riesz transforms in one dimension.
    (dvi, pdf, ps) arXiv: math.AP/0609429


    Links with other web sites:

  • Department of Mathematics, Macquarie University

  • Department of Mathematical Sciences, New Mexico State University

  • School of Mathematical Sciences, A.N.U.

  • The Abstract Analysis and Geometry Program

  • some other harmonic analysts on the Web (by Terence Tao)

    Email Address

    Postal Address
    Mathematics Dept
    Macquarie University, NSW 2109, Australia.
    (61-2) 6125 4504
    (61-2) 9850 8114

    Mathematical Sciences Institute, ANU