...by a tubular function (called "fonction tapis" in Thom's and "distance function" in Mather's terminology), and the fibrations and tubular functions associ
...arrow X$ is the fibre projection associated to $T _ { X }$ and the tubular function $\rho _ { X } : T _ { X } \rightarrow \mathbf{R}$ is a continuous mapping s
5 KB (830 words) - 17:44, 1 July 2020
is either non-injective or non-surjective, then $ \lambda \in \sigma ( A) $.
valued function $ R _ {A} ( \lambda ) = ( A- \lambda I ) ^ {-} 1 $,
5 KB (744 words) - 08:22, 6 June 2020
...compact subsets of $\mathbf{C} ^ { n }$ (cf. also [[Entire function|Entire function]]; [[Uniform convergence|Uniform convergence]]). Let $\mathcal H ( \mathbf
It is immediate to show that $\mathcal{F} \mu$ is an entire function. Moreover, since the exponentials are dense in $\mathcal{H} ( \mathbf{C} ^
8 KB (1,132 words) - 14:49, 27 January 2024
...E = \{ z \in \mathbf C ^ { n } : \rho ( z ) < 0 \}$ is given by a defining function $\rho$ of class $C ^ { 2 }$, then one considers the quadratic form
...ly bounded domain $E$ is convex if and only if the Hessian of its defining function is positive semi-definite when restricted to the real tangent plane at any
16 KB (2,533 words) - 09:46, 18 February 2024
...ace]] $\mathcal{H}$ may be viewed as a non-commutative generalization of a function algebra $C _ { 0 } ( \Omega )$ acting as multiplication operators on some $
...niform convergence|uniform convergence]] on compact subsets of $\Omega$ in function algebras. Thus, it can be shown that $M ( A )$ is the strict completion of
17 KB (2,644 words) - 17:46, 1 July 2020
A function $K ( x , y )$, $x , y \in E$, is called a reproducing kernel of such a Hilb
i) for every fixed $y \in E$, the function $K ( x , y ) \in H$;
11 KB (1,680 words) - 17:31, 4 February 2024
where the right hand-side is the usual partial derivative of the function $f\phi^{-1}:\mathbb{R}^n\rightarrow \mathbb{R}$ in the variables $x_1,\dots
...inates is given by $f(m)=\tilde{f}(x_1(m),\dots,x_n(m))$, then $Xf$ is the function given in local coordinates by the expression
8 KB (1,509 words) - 05:24, 22 May 2017
is a finite surjective analytic mapping inducing an isomorphism of the open sets
then any function that is holomorphic on $ U \setminus A $
8 KB (1,143 words) - 16:48, 19 February 2022
...s that a function $f$ is given on $X$ (and also that the variable $y$ is a function of the variable $x$, or that $y$ depends on $x$) and one writes $f:X\to Y$.
...r finally a dependence can exist and remain unknown" . The definition of a function as a correspondence between two arbitrary sets (not necessarily consisting
34 KB (5,509 words) - 22:06, 28 January 2020
and surjective if $ \mathop{\rm Ran} R = B $.
is functional, that is, it is the graph of a function from $ A $
8 KB (1,265 words) - 17:31, 5 June 2020
is a class function on $ G: \chi _ {V} \in { \mathop{\rm CF} } ( G,K ) $.
2) A class function $ \varphi \in { \mathop{\rm CF} } ( G, \mathbf C ) $
11 KB (1,659 words) - 08:43, 26 March 2023
the Poincaré problem, i.e. can any meromorphic function be represented in the form $ f/g $,
pseudoconvex function exhausting it.
10 KB (1,513 words) - 08:23, 6 June 2020
...ecause after all a (partial) differential equation is a relation between a function, its dependent variables and its derivatives up to a certain order. In the
is surjective for all $ m \in M $.
9 KB (1,406 words) - 21:26, 3 January 2021
...] in $s$. Langlands' general theory of Eisenstein series implies that this function has a meromorphic continuation and hence one can "evaluate" at $s = 0$. H
...es certain $L$-functions $L ( \omega , r , s )$ (cf. also [[L-function|$L$-function]]) and the answer to the above questions depends on the behaviour of certai
12 KB (1,817 words) - 15:30, 1 July 2020
...rue for the columns of $A$.) The determinant of $A$ can be considered as a function of its rows:
1) $d$ is a linear function of any row of $A$:
11 KB (1,876 words) - 20:27, 30 November 2016
...by H.R. Fischer [[#References|[a8]]] (1959). With respect to the study of function spaces, limit spaces are more convenient than topological spaces. A more re
...|epimorphism]]; [[Bimorphism|bimorphism]]) if and only if it is injective (surjective, bijective).
57 KB (8,236 words) - 19:41, 20 January 2021
...normal scheme and let $f$ be a rational (meromorphic in the analytic case) function on $X$. A principal Weil divisor is defined canonically:
...he zeros, while $\sum n_W^- W$ is known as the divisor of the poles of the function $f$. The set of principal Weil divisors is a subgroup $Z_p^1(X)$ of the gro
16 KB (2,805 words) - 02:18, 6 January 2022
is the required function and $ f ( t) $
the given function with values in a complex Banach space $ E $;
26 KB (3,943 words) - 20:22, 16 January 2024
...of Abelian varieties, some results involving Drinfel'd modules over global function fields $L$ can be proved, whose analogues over number fields $L$ are far fr
[[L-function|$L$-function]]). The invention and basic theory as well as large parts of the deeper res
19 KB (3,204 words) - 20:11, 14 April 2012
...gic) and the property that every epimorphism (in the categorical sense) is surjective;
...mathbf{B}$ be algebras and $h : \mathbf{A} \twoheadrightarrow \mathbf B$ a surjective homomorphism. Finally, let $F _ { 0 }$ be the smallest $\mathcal{D}$-filter
76 KB (11,425 words) - 02:12, 15 February 2024