...ssociative ring $K$ with a unit, which is a [[Symmetric function|symmetric function]] in its variables, that is, is invariant under all permutations of the var
...mials, which appear in the representations of the symmetric group, are the Schur polynomials ($S$-functions) $S_{\{\lambda\}}$. These are defined for any pa
5 KB (801 words) - 20:34, 13 September 2016
...tions for the commutant lifting theorem and a certain contractive analytic function in the open unit disc. This characterization of all solutions has several d
is a given function in $ L ^ \infty $.
6 KB (815 words) - 09:51, 26 March 2023
...s theory. For such matrices there are different algorithms (N. Levison, I. Schur and others) for inversion. The inverse of a finite Toeplitz matrix $ A =
...TD valign="top"> N.K. Nikolskii (ed.) , ''Toeplitz operators and spectral function theory'' , Birkhäuser (1989) (Translated from Russian)</TD></TR></table>
6 KB (899 words) - 20:27, 17 January 2024
...ver, it is not known (1983), apart from the two-dimensional case, what the
function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...s the theory of a differentiable manifold in the tangent bundle of which a
function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
55 KB (7,564 words) - 16:56, 7 February 2011
The function
...e permutations, and the permanent is a particular case of the Schur matrix function (cf. [[Immanant]])
8 KB (1,228 words) - 19:13, 17 March 2023
...tsev–Petviashvili equation (cf. [[Soliton|Soliton]]) for Grassmannians and Schur functions [[#References|[a30]]], and the modified Korteweg–de Vries equat
1) The system has a Hamiltonian function
13 KB (1,901 words) - 09:09, 26 March 2023
...ss of operators which is one of the most important classes of operators in function theory; it has many applications in different fields of mathematics and app
...unded operator on $\text{l} ^ { 2 }$ if and only if there exists a bounded function $\phi$ on the unit circle $\bf T$ such that $\widehat { \phi } ( j ) = \alp
18 KB (2,757 words) - 00:48, 15 February 2024
.... Vectors belonging to the summands are called homogeneous, and the parity function, defined by $p ( x ) = \overline{0}$ for $x \in V _ { \bar{0} }$ and $p ( x
...e and there exist super analogues of the usual representation theory, e.g. Schur's double centralizer theorem, Young diagrams [[#References|[a4]]].
18 KB (2,722 words) - 17:47, 1 July 2020
then in the function field case the group $ G( K ^ {ab} /K ) $
.../TD> <TD valign="top"> L.V. Kuz'min, "Homotopy of profinite groups, the Schur multiplicator and class field theory" ''Izv. Akad. Nauk SSSR Ser. Mat.'' ,
17 KB (2,620 words) - 07:48, 13 February 2024
...f-adjoint problems, in which by separation of variables an operator-valued function $ {\mathcal L} ( \lambda ) $
...complicated structure of the resolvent of such an operator as an analytic function.
35 KB (5,059 words) - 04:12, 9 May 2022