共查询到20条相似文献,搜索用时 812 毫秒
1.
In some recent works we have developed a new functional calculus for bounded and unbounded quaternionic operators acting on
a quaternionic Banach space. That functional calculus is based on the theory of slice regular functions and on a Cauchy formula
which holds for particular domains where the admissible functions have power series expansions. In this paper, we use a new
version of the Cauchy formula with slice regular kernel to extend the validity of the quaternionic functional calculus to
functions defined on more general domains. Moreover, we show some of the algebraic properties of the quaternionic functional
calculus such as the S-spectral radius theorem and the S-spectral mapping theorem. Our functional calculus is also a natural tool to define the semigroup e
tA
when A is a linear quaternionic operator.
相似文献
2.
Daniel Alpay F. Colombo I. Sabadini 《Mathematical Methods in the Applied Sciences》2014,37(16):2363-2371
The aim of this paper is to show that we can extend the notion of convergence in the norm‐resolvent sense to the case of several unbounded noncommuting operators (and to quaternionic operators as a particular case) using the notion of S‐resolvent operator. With this notion, we can define bounded functions of unbounded operators using the S‐functional calculus for n‐tuples of noncommuting operators. The same notion can be extended to the case of the F‐resolvent operator, which is the basis of the F‐functional calculus, a monogenic functional calculus for n‐tuples of commuting operators. We also prove some properties of the F‐functional calculus, which are of independent interest. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
3.
Yafang Gong 《Advances in Applied Clifford Algebras》2007,17(2):183-200
Some properties of hypercomplex functions (the null solutions of the polynomial Dirac operators in Rn+1) in Clifford Analysis are discussed, their hypercomplex functional calculi for an n-tuple non-commuting self-adjoint operators A are constructed by the use of Cauchy integral formulas, the polynomial approaches to functional calculi are also considered.
Although these hypercomplex function theories have different representative forms, their hypercomplex functional calculi are
the same as the monogenic functional calculus. 相似文献
4.
Following earlier work by Abel and others,
Kummer gave in 1840 functional equations for the polylogarithm function
Li
m
(z) up to
m = 5, but no example for larger
m was known until recently.
We give the first genuine 2-variable functional equation for the
7-logarithm.
We investigate and relate identities for the 3-logarithm given by
Goncharov and Wojtkowiak and deduce a certain family of
functional equations for the 4-logarithm. 相似文献
5.
V. Jeyakumar Ph.D. 《Journal of Optimization Theory and Applications》1986,50(3):525-533
A minimization problem for a functional on a convex subsetC of a normed linear space is considered. Under certain hypotheses, optimality in a certain subset ofC implies the validity of first-order necessary optimality conditions for the problem inC. The result is applied to a problem in optimal periodic control of neutral functional differential equations.This work was partially supported by a grant from Deutsche Forschungsgemeinschaft and by AFOSR under Grant No. AFOSR-84-0398. 相似文献
6.
The purpose of this article is to generalize the theory of stability of functional equations to the case of n‐Banach spaces. In this article, we prove the generalized Hyers–Ulam stabilities of the Cauchy functional equations, Jensen functional equations and quadratic functional equations on n‐Banach spaces. 相似文献
7.
Solutions to the systems of functional Boolean equations are under study. For each of the classes P
2, T
0, T
1, S, T
01, and S
01, the problem is solved of constructing some systems of functional Boolean equations with a given set of functional constants
and one functional variable whose unique solution is a given function of the class under consideration. For an arbitrary nonempty
set F of n-argument Boolean functions, a system of equations with the functional constants ∨ and & is built with F as the solution set. If F is closed under transition to dual functions then the corresponding system can be constructed without functional constants. 相似文献
8.
9.
In the present paper, we establish the stability and the superstability of a functional inequality corresponding to the functional equation fn(xyx) = ∑i+j+k=n fi(x)fj (y)fk(x). In addition, we take account of the problem of Jacobson radical ranges for such functional inequality. 相似文献
10.
A functional Menger system is a set of n-place functions containing n projections and closed under the so-called Menger's composition of n-place functions. We give the abstract characterization for subsets of these functional systems which contain functions having one common fixed point. 相似文献
11.
R. F. Baum 《Journal of Optimization Theory and Applications》1982,36(3):433-449
We consider here control problems in the Mayer form, with a cost functional which is continuous, but not necessarily of classC
1. The usual necessary conditions for such problems cannot be applied, since they require that the cost functional beC
1. We describe a convergence procedure, based upon approximations to the cost functional, that will yield an optimal trajectory to such control systems. Criteria are given which justify that this approximation procedure will yield a trajectory and control, satisfying certain prescribed conditions, which minimize the above cost functional within a specified class of such pairs. Examples are presented. 相似文献
12.
C. Brezinski 《Journal of Approximation Theory》2010,162(12):2290-2302
Let c be a linear functional defined by its moments c(xi)=ci for i=0,1,…. We proved that the nonlinear functional equations P(t)=c(P(x)P(αx+t)) and P(t)=c(P(x)P(xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. This equation relates the polynomials of the family with those of the scaled and shifted family. Other types of nonlinear functional equations whose solutions are formal orthogonal polynomials are also presented. Applications to Legendre and Chebyshev polynomials are given. Then, orthogonality with respect to a definite inner product is studied. When c is an integral functional with respect to a weight function, the preceding functional equations are nonlinear integral equations, and these results lead to new characterizations of orthogonal polynomials on the real line, on the unit circle, and, more generally, on an algebraic curve. 相似文献
13.
It is shown that the order bidual X
~~ of an Archimedean semiprime f -algebra X has a unit element for the Arens multiplication if and only if every positive linear functional on X extends to a positive linear functional on the f -algebra Orth (X) of all orthomorphisms on X. 相似文献
14.
Robert C. James 《Israel Journal of Mathematics》1972,13(3-4):289-300
A relatively easy proof is given for the known theorem that a Banach space is reflexive if and only if each continuous linear
functional attains its sup on the unit ball. This proof simplifies considerably for separable spaces and can be extended to
give a proof that a boundedw-closed subsetX of a complete locally convex linear topological space isw-compact if and only if each continuous linear functional attains its sup onX.
This work was supported in part by National Science Foundation grant GP-28578. 相似文献
15.
A. B. Antonevich 《Journal of Mathematical Sciences》2008,149(4):1345-1358
Functional operators, i.e., sums of weighted shift operators generated by various maps, are considered. For functional operators
with positive coefficients, variational principles for spectral radii are obtained. These principles say that the logarithm
of the spectral radius is the Legendre transform of a certain convex functional T defined on the set of probability vector-valued measures and depending on the original dynamical system and the functional
space considered. In the subexponential case, we obtain the combinatorial structure of the functional T with the help of the corresponding random walk process constructed according to the dynamical system.
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 15, Differential and Functional Differential Equations. Part 1, 2006. 相似文献
16.
P. Maroni 《Periodica Mathematica Hungarica》1990,21(3):223-248
We show that, ifL is regular, semi-classical functional, thenu is also regular and semi-classical for every complex λ, except for a discrete set of numbers depending onL andc. We give the second order linear differential equation satisfied by each polynomial of the orthogonal sequence associated
withu. The cases whereL is either a classical functional (Hermite, Laguerre, Bessel, Jacobi) or a functional associated with generalized Hermite
polynomials are treated in detail.
相似文献
17.
We study the Cauchy problem for the spatially homogenem Boltzmann equation for true Maxwell molecules. Using the Fourier representation introduced by
Bobylev [Bo75],we give a simplified proof of a result proved by
Tanaka [Ta78].Moreover, we show by means of simple geometric properties, that Tanaka functional is an entropy decreasing functional for the Boltzmann equation for Maxwell molecules. 相似文献
18.
In this paper the problems of unique solvability of boundary value problems for infinite functional differential systems and positivity of their solutions are reduced to analysis of scalar functional equations in the space of measurable essentially bounded functions y:[0,+∞)→(−∞,+∞). Efficient tests of the solvability and the positivity are obtained. 相似文献
19.
吴黎明 《应用数学学报(英文版)》2000,16(2):149-161
1.IntroductionandMainResultsAssumethat(Xt),.T(T~NorAl)isaPolishspaceE-valuedMarkovprocess,definedon(fi,F,(R),(ot),(P-c)..E),withitssemigroupoftransitionkernels(Pt).Here(ot)isthesemigroupofshiftsonfisuchthatX.(otw)~X. t(w),Vs,tET;(R)isthenaturalfiltration.Throughoutthispaperweassumethat(Pt)issymmetricandergodicwithrespectto(w.r.t.forshort)aprobabilitymeasurepon(E,e)(eistheBorela--fieldofE),i.e.,.Symmetry:(Ptf,g)~(f,Pig):~isfptgdp,acET,if,gCL'(P);.ErgodicitytFOranyfEL'(P),ifPtf~f… 相似文献
20.
Georges Haddad 《Israel Journal of Mathematics》1981,39(1-2):83-100
The paper gives a necessary and sufficient condition for the existence of monotone trajectories to differential inclusionsdx/dt ∈S[x(t)] defined on a locally compact subsetX ofR
p, the monotonicity being related to a given preorder onX. This result is then extended to functional differential inclusions with memory which are the multivalued case to retarded
functional differential equations. We give a similar necessary and sufficient condition for the existence of trajectories
which reach a given closed set at timet=0 and stay in it with the monotonicity property fort≧0. 相似文献