Publications


 

My research is in harmonic analysis and approximation theory.   In particular, I am interested in:

 

1.     Bases and frames in Hilbert spaces

2.     Weighted inequalities for the Fourier transform

3.     Unique continuation properties of solutions of elliptic equations and systems.

4.     Evaluation of the norms of convolution operators and other sharp constants

5.     Geometric properties of harmonic functions and of solutions of Schrodinger equations 

6.     Restriction properties of the Fourier transform to manifolds of arbitrary co-dimension and the restriction conjecture

7.     Uniform estimates of orthogonal polynomials and special functions  

 

Here is a list of my publications and preprints. 

 

Papers in Professional Journals and preprints

[38]  L. De Carli and J. Edward,    Riesz bases from orthonormal bases by replacement  (2018)  (submitted)

[37]  L. De Carli, D. Gorbachev and S. Tikhonov,     Weighted gradient inequalities and unique continuation problems  (2018) (submitted)

[36]  L. De Carli, A. Mizrahi, A. Tepper   Three problems on exponential bases , Canadian Math. Bullettin (2018) http://dx.doi.org/10.4153/CMB-2018-015-6

 [35]  L. De Carli, P. Vellucci   p-Riesz basis and  quasi-shift  invariant spaces  To appear in the Contemporary Mathematics volume “Proceedings of the AMS Special Sessions "Frames, Harmonic Analysis and Operator Theory"   edited by:   Y. Kim, S. K. Narayan, G.Picioroaga, and E. Weber.

[34]  L.De Carli, A. Mizrahi   Exponential bases on triangular domains (to appear soon)

[33]  L. De Carli, P. Vellucci   Stability results for  Gabor frames and  the p-order hold models  (short version)   Linear Algebra and Its Applications  536C (2018) pp. 186—200, DOI 10.1016/j.laa.2017.09.020

[32]  L.De Carli, P. Vellucci   Stability results for  the n-order hold models  (long version)   

[31] L. De Carli    Exponential bases on multi-rectangles of  Rd, (submitted)

 [30] L. De Carli and Shaikh Goheen Samad  One-parameter groups and discrete Hilbert transform, Canad. Math. Bull. 59 (2016), 497-507

[29] L. De Carli, Dmitriy Gorbachev and Sergey Tikhonov   Pitt inequalities and restriction theorems for the Fourier transform   Revista Mat. Iberoamericana  33, (3) 2017, pp. 789–808. DOI: 10.4171/RMI/955

 [28] L. De Carli and S. Pathak.  Stability of exponential bases on d- dimensional domains  (to appear soon)

[27]   L. De Carli and Z. Hu, Parseval  frames with n+1 elements in R^n    , in: Methods of Fourier analysis and approximation theory,  (Applied and numerical harmonic analysis) Birkhauser (2016 )

23--32,

 

[26]   L. De Carli,  S. Hudson,  Split functions, Fourier transforms and multipliers.    Collect. Math. 66 (2015), no. 2, 297–309. 

 

[25]   L. De Carli , S. Hudson and X. Li,  Minimal potential results for the Schrodinger equation in a slab    Forum Mathematicum,  28    ( 2016), no. 4,  pp 689—712.

 

[24] L. De Carli, D. Gorbachev, and S. Tikhonov,   Pitt's and Boas' inequalities for Fourier and Hankel  Transforms, Journal of Mathematical Analysis and Applications  408,   (2013),  no. 2, 762–774

 

 [23] L. De Carli, A. Kumar , Exponential bases  on two dimensional  trapezoids,   Proc. Amer. Math. Soc. 143 (2015), no. 7, 2893–2903.

 

[22]  D. Bilyk, L. De Carli, A. Petukhov, A. Stokolos and B. D. Wick , On The Scientific Work of Konstantin Ilyich Oskolkov , Recent Advances in Harmonic Analysis and Applications (In Honor of Konstantin Oskolkov), Springer Proceedings in Mathematics (2012)

 

[21]  L. De Carli,  J. Edward, S. Hudson, M. Leckband,  Minimal support results for  Schrodinger's equation,    Forum Math. 27 (2015), no. 1, 343–371

 

[20]  L. De Carli,    On Fourier multipliers over tube domains,  Recent Advances in Harmonic Analysis and Applications (In Honor of Konstantin Oskolkov), Springer Proceedings  in Mathematics (2012), 79 –92.

 

[19]  L. De Carli,  S. Hudson,  A Faber-Krahn inequality for solutions of  Schrodinger's equation,.  Advances in Mathematics 230 (2012), pp. 2416-2427

 

[18]   L. De Carli,  S. Hudson,   A generalization of Bernoulli’s inequality,   Le Matematiche 65 (2010), n. 1 

 

[17]   L. De Carli,  S. Hudson,   Geometric Remarks on  the Level Curves of Harmonic Functions,  Bull. London Math. Soc. 42 (2010), n. 1,   83—95 .

 

[16]   L. De Carli,  M. Ash,  Growth of  L^p Lebesgue constants for convex polyhedra and other regions,     Transaction of the American Math. Soc.  361 (2009), n. 8,   4215--4232.

 

[15]   L. De Carli, Local L^p inequalities for Gegenbauer polynomials,   in  Topics in classical analysis and applications in honor of Daniel Waterman, 73--87, World Sci. Publ., Hackensack, NJ, (2008).

 

[14]   L. De Carli,  On the  L^p-L^q  norm of the Hankel transform and  related operators   J. Math. Anal. Appl. 348 (2008), n. 1, 366--382.  

[13] L. De Carli, S. Hudson,   Unique continuation for nonnegative solutions of Schrödinger type inequalities. J. Math. Anal. Appl. 318 (2006), no 2,   467--471.

[12]   L. De Carli,   Uniform estimates of ultraspherical polynomials of large order Canadian Math. Bullettin. 48 (2005), no 3,   382—393.

               

[11]   L. De Carli and L. Grafakos,  On the restriction conjecture, Michigan Math. J. 52 (2004), no. 1, 163--180.

 

[10]   L. De Carli and T. Okaji, Unique continuation theorems for Schrodinger operators from a sphere,   Houston J. Math. 27 (2001), no. 1, 219--235.

 

[9]   L. De Carli and E. Laeng, On the  (p,p)  norm of monotonic Fourier multipliers, C. R. Acad.  Sci. Paris Sér. I  Math. 330 (2000), no. 8, 657--662.


[8]   L. De Carli and E. Laeng, Sharp  L^p  estimates  for the segment multiplier,  Collect.Math. 51 (2000), no. 3, 309—326.

[7] L. De Carli,  Unique continuation for elliptic operators with non multiple characteristics,  Israel J. Math. 118 (2000), 15--27.

[6]   L. De Carli and T. Okaji,   Strong Unique continuation for the Dirac operator,  Publ.Res. Inst. Math. Sci. 35 (1999), no. 6, 825—846.

[5]   L. De Carli and A. Iosevich, Some sharp restriction theorems for homogeneous  manifolds, J. Fourier Anal. Appl. 4 (1998), no. 1, 105--128.

[4]   L. De Carli and  M. Nacinovich, Unique continuation in abstract  pseudoconcave  CR  manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), no. 1, 27--46.

[3]   L. De Carli Unique continuation for a class of  higher order elliptic operators, Pacific J. Math. 179   (1997), no. 1, 1--10.

[2]   L. De Carli and A. Iosevich, A restriction theorem for flat manifolds of codimension two, Illinois J.  Math. 39 (1995), no. 4, 576--585.

[1]   L. De Carli, L^p  estimates for the Cauchy transform of distributions with respect to convex cones, Rend. Sem. Mat. Univ. Padova 88 (1992), 35--53.

 

 

OTHER PUBLICATIONS  AND PREPRINTS  

 

 

[1]   L. De Carli,    Unique continuation for higher order elliptic operators, Thesis, University of California, Los Angeles, (1993).

 

[2]   L. De Carli,    Funzioni olomorfe a crescenza lenta e problemi non lineari, (holomorphic functions with slow growth and non linear problems),  Thesis,   Universita’ di Roma ``La sapienza",  (1993)

 

 

 

 

               

 

  
 
 

 

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