Kyosi Itô, 1954, when he was a Fellow at the Institute for Advanced Study, Princeton. On August 22, 2006, the International Mathematical Union awarded the Carl Friedrich Gauss Prize at the opening ceremonies of the International Congress of Mathematicians in Madrid, Spain. The prizewinner is Kyosi Itô. The Gauss prize was created to honor mathematicians whose research has had a profound impact ...

Let $$W_0(\mathbb {R})$$ be the Wiener Banach algebra of functions representable by Fourier integrals Lebesgue integrable functions. It is proved in paper that, particular, a trigonometric series $$\sum \nolimits _{k=-\infty }^\infty c_k e^{ikt}$$ an function if and only there exists $$\phi \in W_0(\mathbb such that (k)=c_k$$ , $$k\in \mathbb {Z}$$ . If $$f\in then piecewise linear continuous $...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

A numerical method of second order of accuracy for computing conditional Wiener integrals of smooth functionals of a general form is proposed. The method is based on simulation of Brownian bridge via the corresponding stochastic di¤erential equations (SDEs) and on ideas of the weak-sense numerical integration of SDEs. A convergence theorem is proved. Special attention is paid to integral-type f...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

We establish characterizations of the radial weights ? on unit disc such that Bergman projection P?, induced by ?, is bounded and/or acts surjectively from L? to Bloch space B, or dual weighted A?1 isomorphic under A?2-pairing. also solve problem posed Dostani? in 2004 describing P? Lebesgue L?p, a weak regularity hypothesis weight involved. With regard Littlewood-Paley estimates, we characteri...

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.

Polynomial interpolation is a classical method to approximate continuous functions by polynomials. To measure the correctness of the approximation, Lebesgue constants are introduced. For a given node system X = {x1 < . . . < xn+1} (xj ∈ [a, b]), the Lebesgue function λn(x) is the sum of the modulus of the Lagrange basis polynomials built on X. The Lebesgue constant Λn assigned to the function λ...