In mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert...

analysis included the construction of Fredholm determinants, and the proof of the Fredholm theorems. Fredholm was a member of the Finnish Society of...

mathematics Analytic Fredholm theorem, in mathematics Fredholm theory, in mathematics Fredholm (crater), a small lunar impact crater 21659 Fredholm (1999 PR3)...

Fredholm's theorem (linear algebra) Analytic Fredholm theorem (functional analysis) Banach–Alaoglu theorem (functional analysis) Banach–Mazur theorem...

theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index...

index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules...

has constant diagonals. Theorem: If g {\displaystyle g} is continuous, then T g − λ {\displaystyle T_{g}-\lambda } is Fredholm if and only if λ {\displaystyle...

Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann...

and then applies mean curvature flow and the Sard–Smale Theorem on regular values of Fredholm operators to prove a contradiction for a surface with a...

integral and differential form. See also, for example, Green's function and Fredholm theory. Various classification methods for integral equations exist. A...

Sparse modeling tool for analytic continuation of imaginary-time Green’s function. Analytic continuation Monodromy theorem Fredholm integral equation Green's...

theory of analytic functions in solving the problem of uniformization of algebraic functions, contributions on formulation of the theorem of analytic extension...

conjecture. With Hirzebruch he extended the Grothendieck–Riemann–Roch theorem to complex analytic embeddings, and in a related paper they showed that the Hodge...

study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems have been produced by Mark Krein, Israel Gohberg...

methods can be found in Hayman (1994). The Grunsky operators and their Fredholm determinants are also related to spectral properties of bounded domains...

general spaces, resulting in a geometrical and analytical apparatus now usually known as the Riesz–Fischer theorem. Further basic results were proved in the...

operators. Cartesian geometry see analytic geometry Calculus An area of mathematics connected by the fundamental theorem of calculus. Calculus of infinitesimals...

situations, which however only work for particular kinds of operators. The Fredholm determinant defines the determinant for operators known as trace class...

Spectral theorem Spectral theory of compact operators Spectral theory of normal C*-algebras Sturm–Liouville theory, Integral equations, Fredholm theory...

Such an integral equation is known as a Fredholm integral equation, the study of which constitutes Fredholm theory. The primary use of Green's functions...

of quasi-analytic functions. He proved the necessary and sufficient condition for quasi-analyticity, now called the Denjoy–Carleman theorem. As a corollary...

first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts...

expected the proof of the Riemann Hypothesis would be a consequence of Fredholm's work on integral equations with a symmetric kernel. His collected works...

factors. In 1951, he expanded the Bernstein theorem; and from this, the properties of the coefficients of the Fredholm determinant of linear integral equations...

which are harmonic. The key technical work is in the establishment of a Fredholm theory for the Laplace-Beltrami operator, when acting between certain Banach...

prove the existence locally of isothermal coordinates on a surface with analytic Riemannian metric. Various techniques have been developed for solving the...

the general linear group. Helton & Howe (1975) gave an analytic way to establish this index theorem, simplied later by Howe. Their proof relies on the fact...

a co-author. With regard to the red book, actually entitled Riesz and Fredholm Theory in Banach Algebras and published by Pitman in 1982, Roger Smyth...

program. The origins of the conjecture go back to Fredholm theory, the Atiyah–Singer index theorem and the interplay of geometry with operator K-theory...

Bruhat, H. Cartan et B. Malgrange (real analytic geometry) André Weil, Sur le théorème de Torelli (Torelli theorem) Claude Chevalley, La notion de correspondance...