-
1
-
-
0001119849
-
Seminaire de Probabilities XIX
-
New York: Springer
-
D. Bakry and M. Emery, “Seminaire de Probabilities XIX,” in Lecture Notes in Mathematics, 1123. New York: Springer, 1985, pp. 179–206.
-
(1985)
Lecture Notes in Mathematics, 1123
, pp. 179-206
-
-
Bakry, D.1
Emery, M.2
-
2
-
-
0000061719
-
Entropy and the central limit theorem
-
A. Barron, “Entropy and the central limit theorem,” Ann. Probab., vol. 14, no. 1, pp. 336–342, 1986.
-
(1986)
Ann. Probab.
, vol.14
, Issue.1
, pp. 336-342
-
-
Barron, A.1
-
3
-
-
0000898117
-
Inequalities in Fourier analysis
-
W. Beckner, “Inequalities in Fourier analysis,” Ann. Math., vol. 102, 159–182, 1975.
-
(1975)
Ann. Math.
, vol.102
, pp. 159-182
-
-
Beckner, W.1
-
4
-
-
0005112588
-
Notes on matrix theory—IV: An inequality due to Bergstrøm
-
R. Bellman, “Notes on matrix theory—IV: An inequality due to Bergstr0m,” Amer. Math. Monthly, vol. 62, pp. 172–173, 1955.
-
(1955)
Amer. Math. Monthly
, vol.62
, pp. 172-173
-
-
Bellman, R.1
-
5
-
-
0016037985
-
A simple converse for broadcast channels with additive white normal noise
-
P. P. Bergmans, “A simple converse for broadcast channels with additive white normal noise,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 279–280, 1974.
-
(1974)
IEEE Trans. Inform. Theory
, vol.IT-20
, pp. 279-280
-
-
Bergmans, P.P.1
-
6
-
-
84938171492
-
The convolution inequality for entropy powers
-
Apr.
-
N. Blachman, “The convolution inequality for entropy powers,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 267–271, Apr. 1965.
-
(1965)
IEEE Trans. Inform. Theory
, vol.IT-11
, pp. 267-271
-
-
Blachman, N.1
-
7
-
-
0001825505
-
Some inequalities for Gaussian measures and the long range order of the one dimensional plasma
-
A. M. Arthors, Ed. Oxford: Clarendon Press
-
H. J. Brascamp and E. J. Lieb, “Some inequalities for Gaussian measures and the long range order of the one dimensional plasma,” in Functional Integration and Its Applications, A. M. Arthors, Ed. Oxford: Clarendon Press, 1975.
-
(1975)
Functional Integration and Its Applications
-
-
Brascamp, H.J.1
Lieb, E.J.2
-
8
-
-
0001126703
-
Best constants in Young’s inequality, its converse and its generalization to more than three functions
-
H. J. Brascamp and E. J. Lieb, “Best constants in Young’s inequality, its converse and its generalization to more than three functions,” Adv. Math., vol. 20, pp. 151–173, 1976.
-
(1976)
Adv. Math.
, vol.20
, pp. 151-173
-
-
Brascamp, H.J.1
Lieb, E.J.2
-
9
-
-
49549132663
-
On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
-
H. J. Brascamp and E. J. Lieb, “On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation,” J. Functional Anal., vol. 22, pp. 366–389, 1976.
-
(1976)
J. Functional Anal.
, vol.22
, pp. 366-389
-
-
Brascamp, H.J.1
Lieb, E.J.2
-
11
-
-
0000458474
-
Some integral identities and inequalities for entire functions and their application to the coherent state transform
-
E. A. Carlen, “Some integral identities and inequalities for entire functions and their application to the coherent state transform,” J. Functional Anal., 1991.
-
(1991)
J. Functional Anal.
-
-
Carlen, E.A.1
-
12
-
-
0000273265
-
Superadditivity of Fisher’s information and logarithmic Sobolev inequalities
-
E. A. Carlen, “Superadditivity of Fisher’s information and logarithmic Sobolev inequalities,” J. Functional Anal., 1991.
-
(1991)
J. Functional Anal.
-
-
Carlen, E.A.1
-
13
-
-
33746710570
-
Entropy production by convolution and central limit theorems with strong rate information
-
E. A. Carlen and A. Soffer, “Entropy production by convolution and central limit theorems with strong rate information,” Commun. Math. Phys., 1991.
-
(1991)
Commun. Math. Phys.
-
-
Carlen, E.A.1
Soffer, A.2
-
14
-
-
0021519553
-
On the similarity of the entropy power inequality and the Brunn-Minkowski inequality
-
M. Costa and T. M. Cover, “On the similarity of the entropy power inequality and the Brunn-Minkowski inequality,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 837–839, 1984.
-
(1984)
IEEE Trans. Inform. Theory
, vol.IT-30
, pp. 837-839
-
-
Costa, M.1
Cover, T.M.2
-
15
-
-
0022148899
-
A new entropy power inequality
-
M. H. M. Costa, “A new entropy power inequality,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 751–760, 1985.
-
(1985)
IEEE Trans. Inform. Theory
, vol.IT-31
, pp. 751-760
-
-
Costa, M.H.M.1
-
16
-
-
0000097117
-
Determinant inequalities via information theory
-
July
-
T. M. Cover and J. A. Thomas, “Determinant inequalities via information theory,” SIAM J. Matrix Anal. and its Applicat., vol. 9, no. 3, pp. 384–392, July 1988.
-
(1988)
SIAM J. Matrix Anal. and its Applicat.
, vol.9
, Issue.3
, pp. 384-392
-
-
Cover, T.M.1
Thomas, J.A.2
-
17
-
-
0020849106
-
An information theoretic proof of Hadamard’s inequality
-
Nov.
-
T. M. Cover and A. El Gamal, “An information theoretic proof of Hadamard’s inequality,” IEEE Trans. Inform. Theory, vol. IT-29, pp. 930–931, Nov. 1983.
-
(1983)
IEEE Trans. Inform. Theory
, vol.IT-29
, pp. 930-931
-
-
Cover, T.M.1
El Gamal, A.2
-
18
-
-
0009028447
-
Informationstheoretische konvegenenzbegriffe im raum der vahrscheinlichkeitsverteilungen
-
VII, ser. A
-
I. Csiszar, “Informationstheoretische konvegenenzbegriffe im raum der vahrscheinlichkeitsverteilungen,” Publ. Math. Inst., Hungarian Academy of Sci., VII, ser. A, pp. 137–157, 1962.
-
(1962)
Publ. Math. Inst., Hungarian Academy of Sci.
, pp. 137-157
-
-
Csiszar, I.1
-
19
-
-
0024704122
-
A simple proof of the concavity of the entropy power with respect to the variance of additive normal noise
-
July
-
A. Dembo, “A simple proof of the concavity of the entropy power with respect to the variance of additive normal noise,” IEEE Trans. Inform. Theory, vol. 35, pp. 887–888, July 1989.
-
(1989)
IEEE Trans. Inform. Theory
, vol.35
, pp. 887-888
-
-
Dembo, A.1
-
20
-
-
25744440940
-
Information inequalities and uncertainty principles
-
A. Dembo, “Information inequalities and uncertainty principles,” Tech. Rep., Dept. of Statist., Stanford Univ., Stanford, CA, 1990.
-
(1990)
Tech. Rep., Dept. of Statist., Stanford Univ., Stanford, CA
-
-
Dembo, A.1
-
21
-
-
0001616908
-
Uncertainty principles and signal recovery
-
D. L. Donoho and P. B. Stark, “Uncertainty principles and signal recovery,” SIAM J. Appl. Math., vol. 49, pp. 906–931, 1989.
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 906-931
-
-
Donoho, D.L.1
Stark, P.B.2
-
22
-
-
0006623358
-
On a theorem of Weyl concerning the eigenvalues of linear transformations II
-
K. Fan, “On a theorem of Weyl concerning the eigenvalues of linear transformations II,” Proc. National Acad. Sci. U.S., vol. 36, 1950, 31–35.
-
(1950)
Proc. National Acad. Sci. U.S
, vol.36
, pp. 31-35
-
-
Fan, K.1
-
23
-
-
0000441920
-
Some inequalities concerning positive-definite matrices
-
K. Fan, “Some inequalities concerning positive-definite matrices,” Proc. Cambridge Phil. Soc., vol. 51, 1955, pp. 414–421.
-
(1955)
Proc. Cambridge Phil. Soc.
, vol.51
, pp. 414-421
-
-
Fan, K.1
-
25
-
-
0001429116
-
Logarithmic Sobolev inequalities
-
L. Gross, “Logarithmic Sobolev inequalities,” Amer. J. Math., vol. 97, pp. 1061–1083, 1975.
-
(1975)
Amer. J. Math.
, vol.97
, pp. 1061-1083
-
-
Gross, L.1
-
26
-
-
84914020419
-
Logarithmic Sobolev inequalities for the heat kernel on a Lie group
-
L. Gross, “Logarithmic Sobolev inequalities for the heat kernel on a Lie group,” in Wite Noise Analysis. Singapore: World Scientific, 1990.
-
(1990)
Wite Noise Analysis
-
-
Gross, L.1
-
27
-
-
0001049514
-
Nonnegative entropy measures of multivariate symmetric correlations
-
T. S. Han, “Nonnegative entropy measures of multivariate symmetric correlations,” Inform. Contr., vol. 36. pp. 133–156, 1978.
-
(1978)
Inform. Contr.
, vol.36
, pp. 133-156
-
-
Han, T.S.1
-
28
-
-
0001542262
-
A note on entropy
-
I. I. Hirschman, “A note on entropy,” Amer. J. Math., vol. 79, pp. 152–156, 1957.
-
(1957)
Amer. J. Math.
, vol.79
, pp. 152-156
-
-
Hirschman, I.I.1
-
29
-
-
84941465845
-
A lower bound for discrimination information in terms of variation
-
S. Kullback, “A lower bound for discrimination information in terms of variation,” IEEE Trans. Inform. Theory, vol. IT-4, pp. 126–127, 1967.
-
(1967)
IEEE Trans. Inform. Theory
, vol.IT-4
, pp. 126-127
-
-
Kullback, S.1
-
30
-
-
0002303432
-
Proof of an entropy conjecture of Wehrl
-
E. H. Lieb, “Proof of an entropy conjecture of Wehrl,” Commun. Math. Phys., vol. 62, pp. 35–41, 1978.
-
(1978)
Commun. Math. Phys.
, vol.62
, pp. 35-41
-
-
Lieb, E.H.1
-
31
-
-
0000201926
-
Gaussian kernels have Gaussian maximizers
-
E. H. Lieb, “Gaussian kernels have Gaussian maximizers.” Inventions Math., vol. 102, pp. 179–208, 1990.
-
(1990)
Inventions Math.
, vol.102
, pp. 179-208
-
-
Lieb, E.H.1
-
33
-
-
34848881795
-
A convexity proof of Hadamard’s inequality
-
A. Marshall and I. Olkin, “A convexity proof of Hadamard’s inequality,” Amer. Math. Monthly, vol. 89, pp. 687–688. 1982.
-
(1982)
Amer. Math. Monthly
, vol.89
, pp. 687-688
-
-
Marshall, A.1
Olkin, I.2
-
34
-
-
84891683949
-
Diskontinuitátsbereich für arithmetische äquivalenz
-
H. Minkowski, “Diskontinuitátsbereich für arithmetische äquivalenz,” J. für Math., vol. 129, pp. 220–274, 1950.
-
(1950)
J. für Math.
, vol.129
, pp. 220-274
-
-
Minkowski, H.1
-
35
-
-
34250546697
-
On a generalization of Hadamard’s determinantal inequality due to Szasz
-
L. Mirsky, “On a generalization of Hadamard’s determinantal inequality due to Szasz,” Arch. Math., vol. 8, pp. 274–275, 1957.
-
(1957)
Arch. Math.
, vol.8
, pp. 274-275
-
-
Mirsky, L.1
-
36
-
-
84962994010
-
Inequalities connected with definite Hermitian forms
-
A. Oppenheim, “Inequalities connected with definite Hermitian forms,” J. Lon. Math. Soc., vol. 5, pp. 114–119, 1930.
-
(1930)
J. Lon. Math. Soc.
, vol.5
, pp. 114-119
-
-
Oppenheim, A.1
-
37
-
-
84940644968
-
A mathematical theory of communication
-
C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp, 379–423, 623–656, 1948.
-
(1948)
Bell Syst. Tech. J.
, vol.27
-
-
Shannon, C.E.1
-
38
-
-
12944295719
-
Some inequalities satisfied by the quantities of information of Fisher and Shannon
-
A. Stam, “Some inequalities satisfied by the quantities of information of Fisher and Shannon,” Inform. Contr., vol. 2. pp. 101–112, 1959.
-
(1959)
Inform. Contr.
, vol.2
, pp. 101-112
-
-
Stam, A.1
-
39
-
-
5844266551
-
General properties of entropy
-
A. Wehrl, “General properties of entropy,” Rev. Modern Phys., vol. 50, pp. 221-260, 1978.
-
(1978)
Rev. Modern Phys.
, vol.50
, pp. 221-260
-
-
Wehrl, A.1
-
40
-
-
0013001769
-
A class of definitions of ‘duration’ (or ‘uncertainty’) and the associated uncertainty relations
-
M. Zakai, “A class of definitions of ‘duration’ (or ‘uncertainty’) and the associated uncertainty relations,” Inform. Contr., vol. 3, pp. 101–115, 1960.
-
(1960)
Inform. Contr.
, vol.3
, pp. 101-115
-
-
Zakai, M.1
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