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J., 22, 525–542 (1955).",{"EN":450},"We propose an asymptotic method for the integration of one type of systems of linear differential equations with a small parameter in the coefficients of a part of derivatives.",{"EN":452},"On the Asymptotic Integration of a System of Linear Differential Equations with a Small Parameter in the Coefficients of a Part of Derivatives",{"VOID":454},"10.1023\u002FA:1024044425018","http:\u002F\u002Flink.springer.com\u002F10.1023\u002FA:1024044425018",[457],{"id":458,"sortIndex":21,"researcher":20,"roles":459,"affiliations":460,"properties":471},"f1752b3c-2173-465a-8496-cb534afc883c",[390],[461],{"id":20,"sortIndex":21,"affiliation":462,"properties":20},{"id":463,"createTime":464,"updateTime":465,"relativeEntities":466,"slug":467,"properties":468,"entityType":41,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"15d342ce-a762-46ce-a595-454b8ab9bc61","2024-01-15T23:51:15.471+00:00","2024-10-12T11:12:57.070+00:00",[],"Institute-of-Mathematics-Ukrainian-Academy-of-Sciences-Kiev",{"title":469},{"VI":470},"Institute of Mathematics, Ukrainian Academy of Sciences, Kiev",{"title":472},{"VI":473},"A. 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Anderson, “On sums of symmetrically dependent random variables,” Skand. Aktuarietidskr.,36, 123–138 (1953).\nE. S. Shtatland, “The distribution of the time of reaching the maximum for a process with independent increments,” Teor. Veroyatn. Ee Primen.,11, No. 4, 720–726 (1966).\nE. A. Pecherskii and B. A. Rogozin, “On the joint distributions of random variables connected with fluctuations of a process with independent increments,” Teor. Veroyatn. Ee Primen.,14, No. 3, 431–441 (1969).\nA. V. Skorokhod, Studies in the Theory of Random Processes, Addison-Wesley (1965).\nA. A. Borovkov, Lectures in Probability Theory [in Russian], Nauka, Moscow (1972).\nD. V. Husak, “Distribution of time of sojourn of homogeneous process with independent increments above an arbitrary level,” Dop. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 14–17 (1981).\nD. V. Gusak, “Boundary functionals for sums of a random number of terms,” in: Analytic Methods in the Theory of Random Processes [in Russian], Inst. Mat., Akad. Nauk Ukr. 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V. Horodets’kyi and O. V. Martynyuk, Parabolic Pseudodifferential Equations with Analytic Symbols in the Spaces of Type S [in Ukrainian], Tekhnodruk, Chernivtsi (2019).\nV. V. Horodets’kyi and O. V. Martynyuk, Cauchy Problem and Nonlocal Problems for Evolutionary Equations of the First Order with Respect to the Time Variable [in Ukrainian], Rodovid, Chernivtsi (2015).\nI. M. Gelfand and G. E. Shilov, Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).\nV. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).\nM. L. Gorbachuk and P. I. Dudnikov, “On the initial data of the Cauchy problem for parabolic equations for which the solutions are infinitely differentiable,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 4, 9–11 (1981).\nV. V. Horodets’kyi, Limit Properties of the Solutions of Parabolic-Type Equations Smooth in a Layer [in Ukrainian], Ruta, Chernivtsi (1998).\nV. V. Horodets’kyi, Sets of Initial Values of Smooth Solutions of Differential-Operator Equations of the Parabolic Type [in Ukrainian], Ruta, Chernivtsi (1998).\nV. V. Horodets’kyi, Evolutionary Equations in Countably Normed Spaces of Infinitely Differentiable Functions [in Ukrainian], Ruta, Chernivtsi (2008).\nI. M. Gelfand and G. E. Shilov, Some Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).\nB. L. Gurevich, “Some spaces of test and generalized functions and the Cauchy problem for finite-difference schemes,” Dokl. Akad. Nauk SSSR, 99, No. 6, 893–896 (1954).\nV. V. Gorodetskii, N. I. Nagnibida, and P. P. Nastasiev, Methods for the Solution of Problems of Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).\nS. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some Their Applications [in Russian], Nauka Tekhnika, Minsk (1987).\nV. V. Horodets’kyi, Ya. M. Drin’, and M. I. Nahnybida, Generalized Functions. Methods for the Solution of Problems [in Ukrainian], Knyhy-XXI, Chernivtsi (2011).",{"EN":588},"We study an evolutionary equation with an operator (i∂\u002F∂x), where φ is a smooth function satisfying certain conditions. As special cases of this equation, we get a partial differential equation of parabolic type with derivatives of finite and infinite orders and an equation with certain operators of fractional differentiation. It is shown that the restriction of the operator (i∂\u002F∂x) to some spaces of type S coincides with a pseudodifferential operator constructed according to the function φ regarded as a symbol. We establish the correct solvability of a nonlocal multipoint (in time) problem for an equation of this kind with an initial function, which is an element of the space of generalized functions of ultradistribution type. The properties of the fundamental solution of this problem are analyzed.",{"EN":590},"Evolutionary Pseudodifferential Equations with Smooth Symbols in S-Type Spaces",{"VOID":592},"10.1007\u002Fs11253-023-02233-3","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11253-023-02233-3",[595,611,623],{"id":596,"sortIndex":597,"researcher":20,"roles":598,"affiliations":599,"properties":608},"5fbfc9b2-cd10-4c89-a9e7-ccf6d7168c8f",2,[390],[600],{"id":20,"sortIndex":21,"affiliation":601,"properties":20},{"id":602,"createTime":603,"updateTime":603,"relativeEntities":604,"slug":20,"properties":605,"entityType":41,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"c33f13f4-1bac-4a94-89f6-5af81332a11f","2023-12-08T01:12:06.152+00:00",[],{"title":606},{"VI":607},"Fed’kovych Chernivtsi National University, Chernivtsi, Ukraine",{"title":609},{"VI":610},"Olha 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