In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential...

introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. The Hilbert transform of u can...

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...

Unsolved problem in mathematics Do all non-trivial zeroes of the Riemann zeta function have a real part of one half? More unsolved problems in mathematics...

surjective. This problem is more commonly called the Riemann–Hilbert problem. It led to several bijective correspondences known as 'Riemann–Hilbert correspondences'...

generalizations of this. The original setting appearing in Hilbert's twenty-first problem was for the Riemann sphere, where it was about the existence of systems...

In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint...

English translation of Hilbert's original address Bombieri, Enrico (2006), "The Riemann Hypothesis", The Millennium Prize Problems, Clay Mathematics Institute...

Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture...

the inverse scattering problem is equivalent to a Riemann-Hilbert problem. Inverse scattering has been applied to many problems including radiolocation...

sphere Riemann–Hilbert correspondence Riemann–Hilbert problem Riemann–Lebesgue lemma Riemann–Liouville integral Riemann–Roch theorem Arithmetic Riemann–Roch...

who rediscovered it as a main ingredient of his solution of the Riemann–Hilbert problem in 1908. Let C be a smooth closed simple curve in the plane, and...

Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge...

1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing...

on ordinary differential equations especially Hilbert's twenty-first problem (Riemann–Hilbert problem). Bolibrukh was the author of about a hundred research...

equations by previously known monodromy matrices is one of the Hilbert problems. Riemann made some famous contributions to modern analytic number theory...

arise from Hilbert–Schmidt operators. The general spectral theorem for self-adjoint operators involves a kind of operator-valued Riemann–Stieltjes integral...

asymptotically the solution of the given Riemann–Hilbert problem to that of a simpler, explicitly solvable, Riemann–Hilbert problem. Cauchy's theorem is used to justify...

Navier–Stokes existence and smoothness P versus NP Riemann hypothesis Yang–Mills existence and mass gap The seventh problem, the Poincaré conjecture, was solved by...

Weierstrass found a flaw in Riemann's argument, and a rigorous proof of existence was found only in 1900 by David Hilbert, using his direct method in...

physics, we may mention the reinterpretation of renormalization as a Riemann–Hilbert problem, the fact that the Slavnov–Taylor identities of gauge theories...

Birkhoff (1909) on the Riemann–Hilbert problem. Atiyah (1957) gave the classification of vector bundles on elliptic curves. The Riemann–Roch theorem for vector...

including applications to the theory of Shimura varieties and the Riemann-Hilbert problem for p-adic varieties." (with Edward Frenkel) "Gerbal Representations...

The DBAR problem is of key importance in the theory of integrable systems, Schrödinger operators and generalizes the Riemann–Hilbert problem. Ablowitz...

rank n vector bundle over the Riemann sphere). For generic monodromy data, the answer to Hilbert's twenty-first problem is 'yes'. The first proof was...

Arakelov theory Grothendieck–Riemann–Roch theorem Hirzebruch–Riemann–Roch theorem Kawasaki's Riemann–Roch formula Hilbert polynomial Moduli of algebraic...

asymptotically the solution of the given Riemann–Hilbert problem to that of a simpler, explicitly solvable, Riemann–Hilbert problem. Cauchy's theorem is used to justify...

. The inverse problem, of constructing the equation (with regular singularities), given a representation, is a Riemann–Hilbert problem. For a regular...

solutions of ODEs in Floquet theory. Floquet theory Monodromy Riemann–Hilbert problem Grass, Dieter; Caulkins, Jonathan P.; Feichtinger, Gustav; Tragler...

spectral theory, integrable systems, random matrix theory and Riemann–Hilbert problems. Deift was born in Durban, South Africa, where he obtained degrees...