Results 1 to 10 of about 17,741 (69)
Improving estimates for discrete polynomial averages [PDF]
, 2020 For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers.
Han, Rui +4 more
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Rains, Eric M., van de Bult, Fokko J.
core +5 more sources
Riemann sums over polytopes [PDF]
, 2006 We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes.Comment: 13 ...
Guillemin, Victor, Sternberg, Shlomo
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THE INEQUALITIES OF HELDER AND MINKOVSKY AND THEIR GENERALIZATIONS
Фізико-математична освітаFormulation of the Problem. A large amount of mathematical literature is devoted to classical inequalities. Helder's inequalities, a special case of which is the Cauchy-Buniakovsky inequality, as well as Minkowski's, which is a polygon inequality in a ...
Yuriy Bokhonov
doaj +1 more source
Thirty-two Goldbach Variations
, 2005 We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby ...
Abramowitz M. +30 more
core +1 more source
, 2013 It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier ...
Goginava, U. +2 more
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Moment conditions in strong laws of large numbers for multiple sums and random measures
, 2017 The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$, where $Z$ is the ...
Brunk +23 more
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Entanglement entropy for non-coplanar regions in quantum field theory
, 2011 We study the entanglement entropy in a relativistic quantum field theory for regions which are not included in a single spatial hyperplane. This geometric configuration cannot be treated with the Euclidean time method and the replica trick.
Blanco, David D., Casini, Horacio
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Gaussian Subordination for the Beurling-Selberg Extremal Problem [PDF]
, 2011 We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type.
Carneiro, Emanuel +2 more
core
Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator
, 2016 We derive explicit inequalities for sums of eigenvalues of one-dimensional Schr\"{o}dinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit as the number ...
Freitas, Pedro, Kennedy, James B.
core +1 more source