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Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
Trivial, strongly minimal theories are model complete after naming constants
model complete naming constants
2015/9/25
We prove that if M is any model of a trivial, strongly
minimal theory, then the elementary diagram Th(MM ) is a model
complete LM -theory. We conclude that all countable models of
a trivial, strong...
There exist multilinear Bohnenblust-Hille constants $(C_{n})_{n=1}^{\infty}$ with $\displaystyle \lim_{n\rightarrow \infty}(C_{n+1}-C_{n}) =0.$
Bohnenblust–Hille inequality Functional Analysis
2012/7/11
The multilinear version of the Bohnenblust-Hille inequality asserts that for every positive integer $m\geq1$ there exists a sequence of positive constants $C_{m}\geq1$ such that% \[(\sum\limits_{i_{1}...
Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality
Absolutely summing operators Bohnenblust–Hille Theorem Functional Analysis
2011/9/20
Abstract: A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$(\sum\limits_{i_{1},...,i_{n}=1}^{N}|U(e_{i_{^{...
Sharp estimates involving $A_\infty$ and $LlogL$ constants, and their applications to PDE
A1 weights RH1 weights Reverse Holder condition sharp estimates elliptic PDE
2011/8/31
Abstract: It is a well known fact that the union of the Reverse H\"{o}lder classes coincides with the union of the Muckenhoupt classes $A_p$, but the $A_\infty$ constant of the weight $w$, which is a ...
Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform
Uniform constants Hausdorff-Young inequalities Cantor group model scattering transform
2011/1/21
Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. SU(1, 1) nonlinear Fourier transform) were first established by Christ and Kiselev [1],[2]. Later Muscalu, Tao, and...
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2010/12/28
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2011/1/19
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...
Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space
Real analytic approximations Lipschitz constants of functions defined Hilbert space
2011/2/24
Let X be a separable real Hilbert space. We show that for every Lipschitz function f : X ! R, and for every " > 0, there exists a Lipschitz, real analytic function g : X ! R such that |f(x) − g(...
On the Seshadri constants of adjoint line bundles
the Seshadri constants adjoint line bundles
2010/11/9
In the present paper we are concerned with the possible values of Seshadri constants. While in general every positive rational number appears as the local Seshadri constant of some ample line bundle, ...
Best constants in Rosenthal-type inequalities and the Kruglov operator
Rosenthal-type inequalities the Kruglov operator
2010/11/11
Let $X$ be a symmetric Banach function space on $[0,1]$ with the Kruglov property, and let $\mathbf{f}=\{f_k\}_{{k=1}}^n$, $n\ge1$ be an arbitrary sequence of independent random variables in $X$. Thi...
Computing local constants for CM elliptic curves
Computing local constants CM elliptic curves
2010/11/9
For E/k an elliptic curve with CM by O, we determine a formula for (a generalization of) the arithmetic local constant of [4] at almost all primes of good reduction. We apply this formula to the CM c...
Extremal maps in best constants vector theory - Part I: Duality and Compactness
Extremal maps constants vector theory - Part I
2010/11/11
We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser est...
Some improvements on the constants for the real Bohnenblust-Hille inequality
improvements constants real Bohnenblust-Hille inequality
2010/12/6
A classical inequality due to Bohnenblust and Hille states that for every N ∈ N and every m-linear mapping U : ℓN 1 × · · · × ℓN 1 → C we have N X i1,...,im=1 U(ei1 , ..., eim) 2m m...
Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
Caffarelli-Kohn-Nirenberg inequality Gagliardo-Nirenberg inequality loga-rithmic Hardy inequality logarithmic Sobolev inequality
2010/12/14
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WL...