Evaluation of the Fermi-Dirac integral of half-integer order
Exact bounds for some basis functions of approximation operators.
Exactness of the approximation of subharmonic function by the logarithm of the modulus of an analytic function in the Chebyshev metric.
Exemples de formules de quadrature numérique à nombre minimal de noeuds sur des domaines à double symétrie axiale
Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
Existence of an instanton singularity in . Euclidean field theory
Existence of best approximations
Exit criteria and monotonicity in compound quadrature of Gaussian type.
Exotic approximate identities and Maass forms
We obtain some approximate identities whose accuracy depends on the bottom of the discrete spectrum of the Laplace-Beltrami operator in the automorphic setting and on the symmetries of the corresponding Maass wave forms. From the geometric point of view, the underlying Riemann surfaces are classical modular curves and Shimura curves.
Experiment on numerical conformal mapping of unbounded multiply connected domain in fundamental solutions method.
Exponential approximation on the real line
Exponential expressivity of neural networks on Gevrey classes with point singularities
We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains , . We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in , comprising the countably-normed spaces of I. M. Babuška and B. Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high...
Extendability of T* Sets.
Extended Chebyshev systems for the expansions of exp (At).
Extending n-convex functions
We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.
Extending Stechkin's theorem and beyond.
Extension of the best approximation operator in Orlicz spaces.
Extension of the best approximation operator in Orlicz spaces and weak-type inequalities.
Extension via interpolation
We suggest a modification of the Pawłucki and Pleśniak method to construct a continuous linear extension operator by means of interpolation polynomials. As an illustration we present explicitly the extension operator for the space of Whitney functions given on the Cantor ternary set.
Extensions and Selections in Subspaces of C(K).