This paper is the continuation of the work ”On an inverse problem for finite-difference operators of second order” ([1]). We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum. Usin...

This paper is the continuation of the work ”On an inverse problem for finite-difference operators of second order” ([1]). We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum. Usin...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...

In this paper, we study the Cauchy problem for linear and semilinear Moore-Gibson-Thompson (MGT) equation in dissipative case. Concerning MGT model, by utilizing WKB analysis associated with Fourier analysis, derive some $L^2$ estimates of solutions, which improve those previous research [46]. Furthermore, asymptotic profiles solution an approximate relation a framework weighted $L^1$ space are...

The concepts of I-convergence and I-Cauchy condition are a generalization of statistical convergence and statistical Cauchy conditions and are dependent on the notion of the ideal I of subsets of the set N of positive integers. In this paper, we shall introduce two new notions of I-uniform continuity and I-uniform boundedness of a function with values in R or in a metric space and then study th...

shuffle product of the permutations u E E k and v' E E k, we mean the following element from ~+~, /,, (i), i < k , vmv'=: Z o'o(~,| where (v~v') ( i ) = ~ . v , ( i _ k ) + l e ' i ' > k . a(~sk+n'cn} Since the permutations form an additive basis of the space ~ , the shuffle multiplication is uniquely extended "by linearity" to any pair of elements from ~ and defines in $ = ~0$n a structure of ...

We explore a function theory connected with the principal series representation of SL(2, R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. ∗Supported by grant 3GP03196 of the FWO-Vlaanderen (Fund of Scientific ResearchFlanders), Scientif...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...