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The Bonami-Beckner hypercontractive inequality is a powerful tool in Fourier analysis of real-valued functions on the Boolean cube.
Inequalities
G. H. Hardy, J. E. Littlewood, and G. Pólya · 1952
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Étude des coefficients de Fourier des fonctions de L p ( G ) L^{p}(G)
A. Bonami · 1970
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Bounds for the quantity of information transmitted by a quantum communication channel
A. S. Holevo · 1973
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The moduli of smoothness and convexity and the Rademacher averages of trace classes S p ( 1 ≤ p < ∞ ) S_{p}(1\leq p<\infty)
N. Tomczak-Jaegermann · 1974
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Inequalities in Fourier analysis
W. Beckner · 1975
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Logarithmic Sobolev inequalities
L. Gross · 1975
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On the integrability of Banach space valued Walsh polynomials
C. Borell · 1979
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The influence of variables on Boolean functions
J. Kahn, G. Kalai, and N. Linial · 1988
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Optimal hypercontractivity for Fermi fields and related noncommutative integration inequalities
E. A. Carlen and E. H. Lieb · 1993
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Constant depth circuits, Fourier transform, and learnability
N. Linial, Y. Mansour, and N. Nisan · 1993
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Sharp uniform convexity and smoothness inequalities for trace norms
K. Ball, E. Carlen, and E. Lieb · 1994
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The BNS lower bound for multi-party protocols is nearly optimal
Vince Grolmusz · 1994
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An O ( n log log n ) O(n^{\log\log n}) learning algorithm for DNF under the uniform distribution
Y. Mansour · 1995
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Fourier analysis for probabilistic communication complexity
R. Raz · 1995
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Matrix Analysis
R. Bhatia · 1997
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An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space
S. G. Bobkov · 1997
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An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
J. Jackson · 1997
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Communication Complexity
E. Kushilevitz and N. Nisan · 1997
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Quantum vs. classical communication and computation
H. Buhrman, R. Cleve, and A. Wigderson · 1998
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Private information retrieval
B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan · 1998
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Quantum dense coding and a lower bound for 1-way quantum finite automata
A. Ambainis, A. Nayak, A. Ta-Shma, and U. Vazirani · 1999
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Optimal lower bounds for quantum automata and random access codes
A. Nayak · 1999
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On the efficiency of local decoding procedures for error-correcting codes
J. Katz and L. Trevisan · 2000
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Quantum walk on the line
A. Nayak and A. Vishwanath · 2000
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Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
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The cost of the missing bit: Communication complexity with help
L. Babai, T. P. Hayes, and P. G. Kimmel · 2001
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Some applications of coding theory in computational complexity
L. Trevisan · 2004
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A strong direct product theorem for corruption and the multiparty communication complexity of set disjointness
P. Beame, T. Pitassi, N. Segerlind, and A. Wigderson · 2006
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Lower bounds for linear locally decodable codes and private information retrieval
O. Goldreich, H. Karloff, L. Schulman, and L. Trevisan · 2006
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Threshold phenomena and influence
G. Kalai and S. Safra · 2006
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New lower bounds for general locally decodable codes
D. Woodruff · 2006
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Exponential separations for one-way quantum communication complexity, with applications to cryptography
D. Gavinsky, J. Kempe, I. Kerenidis, R. Raz, and R. de Wolf · 2007
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Communication complexity lower bounds by polynomials
H. Buhrman and R. de Wolf · 2001
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Some optimal inapproximability results
J. Håstad · 2001
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Extremal Combinatorics
S. Jukna · 2001
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Lower bounds for quantum communication complexity
H. Klauck · 2001
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Breaking the O ( n 1 / ( 2 k − 1 ) ) O(n^{1/(2k-1)}) barrier for information-theoretic Private Information Retrieval
A. Beimel, Y. Ishai, E. Kushilevitz, and J. Raymond · 2002
Cited alongside, same era.
Improved quantum communication complexity bounds for disjointness and equality
P. Høyer and R. de Wolf · 2002
Cited alongside, same era.
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Sampling of min-entropy relative to quantum knowledge, 28 Dec 2007
R. König and R. Renner · 2007
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Lecture notes for a course “Analysis of Boolean functions”, 2007
R. O’Donnell · 2007
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One-way multi-party communication lower bound for pointer jumping with applications
E. Viola and A. Wigderson · 2007
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Towards 3-query locally decodable codes of subexponential length
S. Yekhanin · 2007
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Multiparty communication complexity of disjointness
A. Chattopadhyay and A. Ada · 2008
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Randomness extraction via delta-biased masking in the presence of a quantum attacker
S. Fehr and C. Schaffner · 2008
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On tensor norms and locally decodable codes, 2008
I. Haviv and O. Regev · 2008
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Direct product theorems for classical communication complexity via subdistribution bounds
R. Jain, H. Klauck, and A. Nayak · 2008
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Lower bounds on quantum multiparty communication complexity, 2008
T. Lee, G. Schechtman, and A. Shraibman · 2008
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Disjointness is hard in the multi-party number-on-the-forehead model
T. Lee and A. Shraibman · 2008
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Noise stability of functions with low influences: invariance and optimality
E. Mossel, R. O’Donnell, and K. Oleszkiewicz · 2008
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Some topics in analysis of boolean functions
R. O’Donnell · 2008
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Personal communication with O. Regev, March 2008
A. Samorodnitsky · 2008
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