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

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...

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...

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)...

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...

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

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

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

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

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

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...

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

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...

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...

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

Hotel Hilbert's problems Hilbert's program Hilbert's syzygy theorem Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Riemann–Hilbert correspondence...

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...

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

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...

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

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...

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...

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

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

field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...

{K^{+}(k){\widehat {g\,}}(k)-G^{+}(k)}{K^{+}(k)F(k,0)}}.} Wiener filter Riemann–Hilbert problem Noble 1958, §4.2. Noble 1958, Chapter 1. "Category:Wiener-Hopf...

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

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...

valid. Later, David Hilbert was able to prove that, to a large extent, the Dirichlet principle is valid under the hypothesis that Riemann was working with...