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.
pdf.

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.
doi:10.1007/s002200050163
pdf.

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.
doi:10.1006/jfan.1998.3361
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.
doi:10.1007/s002090100268
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.
doi:10.1007/s002090100244
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.
doi:10.1016/S0022-1236(02)00009-5
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. (3) 95 (2007), no. 2, 299-328.
(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. 7 (2007), no. 1, 79-112.
(dvi, pdf, ps) arXiv: math.AP/0601350

Derek W. Robinson and Adam Sikora
Degenerate elliptic operators: capacity, flux and separation.
J. Ramanujan Math. Soc. 22 (2007), no. 4, 385-408.
(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
pdf.

Raphael J. Lyman and Adam Sikora
Prediction of bandlimited fading envelopes with arbitrary spectral shape.
IEEE Transactions on Wireless Communications vol. 6, no. 4, April 2007, 1560-1567
pdf.

Derek W. Robinson and Adam Sikora
Analysis of degenerate elliptic operators of Grushin type.
Math. Z. 260 (2008), no. 3, 475-508.
(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 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: Adam.Sikoraatmaths.anu.edu.au
Postal Address: Centre for Mathematics and its Applications, Mathematical Sciences Institute; Australian National University, Canberra, ACT 0200, Australia.
Phone: (61-2) 6125 4504
FAX: (61-2) 6125 5549
Links: Mathematical Sciences Institute, ANU