Pub Date : 2020-10-06DOI: 10.32523/2077-9879-2021-12-3-78-89
Benedetto Silvestri
In this work we establish a Stokes-type integral equality for scalarly essentially integrable forms on an orientable smooth manifold with values in the locally convex linear space $langle B(G),sigma(B(G),mathcal{N})rangle$, where $G$ is a complex Banach space and $mathcal{N}$ is a suitable linear subspace of the norm dual of $B(G)$. This result widely extends the Newton-Leibnitz-type equality stated in one of our previous articles. To obtain our equality we generalize the main result of that article, and employ the Stokes theorem for smooth locally convex vector valued forms established in a prodromic paper. Two facts are remarkable. Firstly the forms integrated involved in the equality are functions of a possibly unbounded scalar type spectral operator in $G$. Secondly these forms need not be smooth nor even continuously differentiable.
{"title":"STOKES-TYPE INTEGRAL EQUALITIES FOR SCALARLY ESSENTIALLY INTEGRABLE LOCALLY CONVEX VECTOR-VALUED FORMS WHICH ARE FUNCTIONS OF AN UNBOUNDED SPECTRAL OPERATOR","authors":"Benedetto Silvestri","doi":"10.32523/2077-9879-2021-12-3-78-89","DOIUrl":"https://doi.org/10.32523/2077-9879-2021-12-3-78-89","url":null,"abstract":"In this work we establish a Stokes-type integral equality for scalarly essentially integrable forms on an orientable smooth manifold with values in the locally convex linear space $langle B(G),sigma(B(G),mathcal{N})rangle$, where $G$ is a complex Banach space and $mathcal{N}$ is a suitable linear subspace of the norm dual of $B(G)$. This result widely extends the Newton-Leibnitz-type equality stated in one of our previous articles. To obtain our equality we generalize the main result of that article, and employ the Stokes theorem for smooth locally convex vector valued forms established in a prodromic paper. Two facts are remarkable. Firstly the forms integrated involved in the equality are functions of a possibly unbounded scalar type spectral operator in $G$. Secondly these forms need not be smooth nor even continuously differentiable.","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46040319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-27DOI: 10.32523/2077-9879-2021-12-4-53-73
B. Khabibullin
Our main results are certain developments of the classical Poisson--Jensen formula for subharmonic functions. The basis of the classical Poisson--Jensen formula is the natural duality between harmonic measures and Green's functions. Our generalizations use some duality between the balayage of measures and and their potentials.
{"title":"POISSON-JENSEN FORMULAS AND BALAYAGE OF MEASURES","authors":"B. Khabibullin","doi":"10.32523/2077-9879-2021-12-4-53-73","DOIUrl":"https://doi.org/10.32523/2077-9879-2021-12-4-53-73","url":null,"abstract":"Our main results are certain developments of the classical Poisson--Jensen formula for subharmonic functions. The basis of the classical Poisson--Jensen formula is the natural duality between harmonic measures and Green's functions. Our generalizations use some duality between the balayage of measures and and their potentials.","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42947150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-31DOI: 10.32523/2077-9879-2019-10-4-47-62
P. D. Lamberti, V. Vespri
We discuss a few old results concerning embedding theorems for Campanato and Sobolev-Morrey spaces adapting the formulations to the case of domains of class $C^{0,gamma}$, and we present more recent results concerning the extension of functions from Sobolev-Morrey spaces defined on those domains. As a corollary of the extension theorem we obtain an embedding theorem for Sobolev-Morrey spaces on arbitrary $C^{0,gamma}$ domains.
{"title":"REMARKS ON SOBOLEV-MORREY-CAMPANATO SPACES DEFINED ON C_{0;gamma} DOMAINS","authors":"P. D. Lamberti, V. Vespri","doi":"10.32523/2077-9879-2019-10-4-47-62","DOIUrl":"https://doi.org/10.32523/2077-9879-2019-10-4-47-62","url":null,"abstract":"We discuss a few old results concerning embedding theorems for Campanato and Sobolev-Morrey spaces adapting the formulations to the case of domains of class $C^{0,gamma}$, and we present more recent results concerning the extension of functions from Sobolev-Morrey spaces defined on those domains. As a corollary of the extension theorem we obtain an embedding theorem for Sobolev-Morrey spaces on arbitrary $C^{0,gamma}$ domains.","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43562713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2077-9879-2020-11-4-08-24
A. Baskakov, V. Strukov, I. Strukova
{"title":"ALMOST PERIODIC AT INFINITY FUNCTIONS FROM HOMOGENEOUS SPACES AS SOLUTIONS TO DIFFERENTIAL EQUATIONS WITH UNBOUNDED OPERATOR COEFFICIENTS","authors":"A. Baskakov, V. Strukov, I. Strukova","doi":"10.32523/2077-9879-2020-11-4-08-24","DOIUrl":"https://doi.org/10.32523/2077-9879-2020-11-4-08-24","url":null,"abstract":"","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2077-9879-2020-11-4-25-34
B. Biyarov, D. Svistunov, G. Abdrasheva
{"title":"CORRECT SINGULAR PERTURBATIONS OF THE LAPLACE OPERATOR","authors":"B. Biyarov, D. Svistunov, G. Abdrasheva","doi":"10.32523/2077-9879-2020-11-4-25-34","DOIUrl":"https://doi.org/10.32523/2077-9879-2020-11-4-25-34","url":null,"abstract":"","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2077-9879-2020-11-4-87-94
V. Burenkov, E. Nursultanov
{"title":"INTERPOLATION THEOREMS FOR NONLINEAR URYSOHN INTEGRAL OPERATORS IN GENERAL MORREY-TYPE SPACES","authors":"V. Burenkov, E. Nursultanov","doi":"10.32523/2077-9879-2020-11-4-87-94","DOIUrl":"https://doi.org/10.32523/2077-9879-2020-11-4-87-94","url":null,"abstract":"","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69697548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-10DOI: 10.32523/2077-9879-2022-13-1-44-68
I. V. Latkin
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense is that there exist two non-equivalent elements. However, at first, we will obtain a lower bound on the computational complexity for the first-order theory of Boolean algebra that has only two elements. For this purpose, we will code the long-continued deterministic Turing machine computations by the relatively short-length quantified Boolean formulae; the modified Stockmeyer and Meyer method will appreciably be used for this simulation. Then, we will transform the modeling formulae of the theory of this Boolean algebra to the simulation ones of the first-order theory of the only equivalence relation in polynomial time. Since the computational complexity of these theories is not polynomial, we obtain that the class $mathbf{P}$ is a proper subclass of $mathbf{PSPACE}$ (Polynomial Time is a proper subset of Polynomial Space). Keywords: Computational complexity, the theory of equality, the coding of computations, simulation by means formulae, polynomial time, polynomial space, lower complexity bound
{"title":"THE RECOGNITION COMPLEXITY OF DECIDABLE THEORIES","authors":"I. V. Latkin","doi":"10.32523/2077-9879-2022-13-1-44-68","DOIUrl":"https://doi.org/10.32523/2077-9879-2022-13-1-44-68","url":null,"abstract":"We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense is that there exist two non-equivalent elements. However, at first, we will obtain a lower bound on the computational complexity for the first-order theory of Boolean algebra that has only two elements. For this purpose, we will code the long-continued deterministic Turing machine computations by the relatively short-length quantified Boolean formulae; the modified Stockmeyer and Meyer method will appreciably be used for this simulation. Then, we will transform the modeling formulae of the theory of this Boolean algebra to the simulation ones of the first-order theory of the only equivalence relation in polynomial time. Since the computational complexity of these theories is not polynomial, we obtain that the class $mathbf{P}$ is a proper subclass of $mathbf{PSPACE}$ (Polynomial Time is a proper subset of Polynomial Space). Keywords: Computational complexity, the theory of equality, the coding of computations, simulation by means formulae, polynomial time, polynomial space, lower complexity bound","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43012379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.32523/2077-9879-2019-10-2-84-92
R. Sengupta, S. Zhukovskiy
{"title":"MINIMA OF FUNCTIONS ON (q1; q2)-QUASIMETRIC SPACES","authors":"R. Sengupta, S. Zhukovskiy","doi":"10.32523/2077-9879-2019-10-2-84-92","DOIUrl":"https://doi.org/10.32523/2077-9879-2019-10-2-84-92","url":null,"abstract":"","PeriodicalId":44248,"journal":{"name":"Eurasian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69697214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：