共查询到20条相似文献,搜索用时 83 毫秒
2.
Summary.
We describe the set of solutions of Wilsons functional equation on any
step 2 nilpotent group and how the set of classical solutions
in certain cases must be supplemented by 4-dimensional spaces of
solutions. 相似文献
3.
4.
5.
6.
7.
8.
9.
Henrik Stetkær 《Aequationes Mathematicae》2017,91(5):945-947
Let S be a semigroup, and \(\mathbb {F}\) a field of characteristic \(\ne 2\). If the pair \(f,g:S \rightarrow \mathbb {F}\) is a solution of Wilson’s \(\mu \)-functional equation such that \(f \ne 0\), then g satisfies d’Alembert’s \(\mu \)-functional equation. 相似文献
10.
11.
12.
13.
In this paper we find a closed form of the solution for the factored inhomogeneous linear equation
Under the hypothesis A
1, A
2, …, A
n
are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach
space X. Here we do not assume that A
j
s are distinct and we offer the computational method to get explicit solutions of certain partial differential equations. 相似文献
14.
Aequationes mathematicae - Roger Cuculière [Problem 11998, The American Mathematical Monthly 124 no. 7 (2017)] has posed the following problem: Find all continuous functions $$f: mathbb R... 相似文献
15.
In this paper we study the solutions of the integral Van Vleck’s functional equation for the sine
$$\begin{aligned} \int _{S}f(x\tau (y)t)d\mu (t)-\int _{S}f(xyt)d\mu (t) =2f(x)f(y),\; x,y\in S \end{aligned}$$and the integral Kannappan’s functional equation
$$\begin{aligned} \int _{S}f(xyt)d\mu (t)+\int _{S}f(x\tau (y)t)d\mu (t) =2f(x)f(y),\; x,y\in S, \end{aligned}$$where S is a semigroup, \(\tau \) is an involution of S and \(\mu \) is a measure that is a linear combination of Dirac measures \((\delta _{z_{i}})_{i\in I}\), such that for all \(i\in I\), \(z_{i}\) is contained in the center of S. We express the solutions of the first equation by means of multiplicative functions on S, and we prove that the solutions of the second equation are closely related to the solutions of d’Alembert’s classic functional equation with involution.
相似文献16.
Aequationes mathematicae - Investigating the future value F(K, s, t) of a capital K invested between dates s and t, the “natural” condition $$F(K,s,t)ge K$$ has lost... 相似文献
17.
We give a classification of maximal subalgebras of rankn−1 for the extended Poincaré algebra
, which is realized on the set of solutions of the d'Alembert equation
. These subalgebras are used for constructing anzatses that reduce this equation to differential equations with two invariant
variables.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 651–662, June, 1994. 相似文献
18.
Thomas A. Ivey 《Results in Mathematics》2011,60(1-4):293-309
A Hopf hypersurface in complex hyperbolic space ${\mathbb{C}{\rm H}^n}$ is one for which the complex structure applied to the normal vector is a principal direction at each point. In this paper, Hopf hypersurfaces for which the corresponding principal curvature is small (relative to ambient curvature) are studied by means of a generalized Gauss map into a product of spheres, and it is shown that the hypersurface may be recovered from the image of this map, via an explicit parametrization. 相似文献
19.
Rados?aw ?ukasik 《Aequationes Mathematicae》2012,83(1-2):75-86
We find the solutions ${f,g,h \colon S \to H}$ of each of the functional equations $$\sum\limits_{\lambda \in \Lambda} f(x+\lambda y)=|\Lambda| g(x)+h(y),\quad x,y\in S,$$ where (S,?+) is an abelian semigroup, Λ is a finite subgroup of the automorphism group of S,?(H,?+) is an abelian group. 相似文献
20.
V. E. Slyusarchuk 《Siberian Mathematical Journal》2017,58(1):159-168
We obtain some conditions for existence of almost periodic solutions for almost periodic functional equations in a Banach space which do not use the H-classes of these equations. 相似文献