Ukrainian Mathematical Journal 

About: Ukrainian Mathematical Journal is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Differential equation & Boundary value problem. It has an ISSN identifier of 0041-5995. Over the lifetime, 8467 publications have been published receiving 27363 citations.

On the space of sequences of p-bounded variation and related matrix mappings

Abstract: The difference sequence spaces l∞(▵), c(▵), and c 0(▵) were studied by Kizmaz. The main purpose of the present paper is to introduce the space bv p consisting of all sequences whose differences are in the space l p , and to fill up the gap in the existing literature. Moreover, it is proved that the space bv p is the BK-space including the space l p . We also show that the spaces bv p and l p are linearly isomorphic for 1 ≤ p ≤ ∞. Furthermore, the basis and the α-, β-, and γ-duals of the space bv p are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv p : l∞), (bv∞ : l p ), and (bv p : l1), and the characterizations of some other matrix classes are obtained by means of a suitable relation.

On Some Euler Sequence Spaces of Nonabsolute Type

Abstract: In the present paper, we introduce Euler sequence spaces e 0 r and e of nonabsolute type that are BK-spaces including the spaces c 0 and c and prove that the spaces e 0 r and e are linearly isomorphic to the spaces c 0 and c, respectively. Furthermore, some inclusion theorems are presented. Moreover, the α-, β-, γ- and continuous duals of the spaces e 0 r and e are computed and their bases are constructed. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes $$\left( {e_c^r :\ell _p } \right)$$ and $$\left( {e_c^r :c} \right)$$ are established, and characterizations of some other classes of infinite matrices are also derived by means of a given basic lemma, where 1 ≤ p ≤ ∞.

On a formula of the generalized resolvents of a nondensely defined Hermitian operator

Abstract: The Weyl function and the prohibited lineal, corresponding to a given space of boundary values of a nondensely defined Hermitian operator, are introduced and investigated. The prohibited lineal is characterized in terms of the limiting values of the Weyl function. An analogue of M. G. Krein's formula for the resolvent is obtained and its connection with the space of boundary values is found.