Pub Date : 2020-06-28DOI: 10.31392/mfat-npu26_2.2020.05
B. Duncan
We consider when the universal C∗-algebras associated to separated graphs are exact. Specifically, for finite separated graphs we show that the universal C∗-algebra is exact if and only if the C∗-algebra is isomorphic to a graph C∗-algebra which occurs precisely when the universal and reduced C∗-algebras of the separated graph are isomorphic.
{"title":"When universal separated graph $C^*$-algebras are exact","authors":"B. Duncan","doi":"10.31392/mfat-npu26_2.2020.05","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2020.05","url":null,"abstract":"We consider when the universal C∗-algebras associated to separated graphs are exact. Specifically, for finite separated graphs we show that the universal C∗-algebra is exact if and only if the C∗-algebra is isomorphic to a graph C∗-algebra which occurs precisely when the universal and reduced C∗-algebras of the separated graph are isomorphic.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"126-140"},"PeriodicalIF":0.4,"publicationDate":"2020-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706760","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 : 2020-06-28DOI: 10.31392/mfat-npu26_2.2020.02
A. Goriunov
The paper investigates spectral properties of multi-interval SturmLiouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions and also all generalized resolvents in terms of boundary conditions are given.
{"title":"Multi-interval Sturm-Liouville problems with distributional coefficients","authors":"A. Goriunov","doi":"10.31392/mfat-npu26_2.2020.02","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2020.02","url":null,"abstract":"The paper investigates spectral properties of multi-interval SturmLiouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions and also all generalized resolvents in terms of boundary conditions are given.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"103-110"},"PeriodicalIF":0.4,"publicationDate":"2020-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48843742","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 : 2020-06-21DOI: 10.31392/MFAT-NPU26_4.2020.06
Y. Kondratiev
We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.
{"title":"Representations of the Infinite-Dimensional Affine Group","authors":"Y. Kondratiev","doi":"10.31392/MFAT-NPU26_4.2020.06","DOIUrl":"https://doi.org/10.31392/MFAT-NPU26_4.2020.06","url":null,"abstract":"We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46886179","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 : 2020-06-12DOI: 10.31392/mfat-npu26_3.2020.05
Kondratiev, G. Yuri, Da Silva, L. Jos'e
In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular and a regular part given in terms of the jump generator. The main technical question is to find a bound for the regular part.
{"title":"Green measures for Markov processes","authors":"Kondratiev, G. Yuri, Da Silva, L. Jos'e","doi":"10.31392/mfat-npu26_3.2020.05","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.05","url":null,"abstract":"In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular and a regular part given in terms of the jump generator. The main technical question is to find a bound for the regular part.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43932706","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 : 2020-03-28DOI: 10.31392/mfat-npu26_1.2020.02
Yuriy M. Dyukarev
Entropy functionals and their extremal values have been studied by many authors (see, for example, [1], [2], [3], [5]). But similar functionals were not considered for solution interpolation problems in the matrix Stieltjes class. In this paper, entropy functionals over solutions of the Stieltjes matrix moment problem are defined and studied for the first time. Given integers m,n ≥ 1, we let C denote the linear space of columns of complex numbers x = col (
{"title":"Entropy functionals and their extremal values for solving the Stieltjes matrix moment problem","authors":"Yuriy M. Dyukarev","doi":"10.31392/mfat-npu26_1.2020.02","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2020.02","url":null,"abstract":"Entropy functionals and their extremal values have been studied by many authors (see, for example, [1], [2], [3], [5]). But similar functionals were not considered for solution interpolation problems in the matrix Stieltjes class. In this paper, entropy functionals over solutions of the Stieltjes matrix moment problem are defined and studied for the first time. Given integers m,n ≥ 1, we let C denote the linear space of columns of complex numbers x = col (","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"27-38"},"PeriodicalIF":0.4,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43156310","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 : 2020-03-28DOI: 10.31392/mfat-npu26_1.2020.04
H. Boua
{"title":"Upper semi-Fredholm and Kato spectrum of an $alpha$-times integrated \u0000semigroup","authors":"H. Boua","doi":"10.31392/mfat-npu26_1.2020.04","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2020.04","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"63-67"},"PeriodicalIF":0.4,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46996120","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 : 2019-12-02DOI: 10.31392/mfat-npu26_1.2020.07
A. Kravchenko, Bohdan Feshchenko
This paper is devoted to the study of special subgroups of the automorphism groups of Kronrod-Reeb graphs of a Morse functions on $2$-torus $T^2$ which arise from the action of diffeomorphisms preserving a given Morse function on $T^2$. In this paper we give a full description of such classes of groups.
{"title":"Automorphisms of Kronrod-Reeb graphs of Morse functions on 2-torus","authors":"A. Kravchenko, Bohdan Feshchenko","doi":"10.31392/mfat-npu26_1.2020.07","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2020.07","url":null,"abstract":"This paper is devoted to the study of special subgroups of the automorphism groups of Kronrod-Reeb graphs of a Morse functions on $2$-torus $T^2$ which arise from the action of diffeomorphisms preserving a given Morse function on $T^2$. In this paper we give a full description of such classes of groups.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41361289","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 : 2019-09-01DOI: 10.31392/MFAT-npu26_1.2020.06
Yuriy Golovaty
We consider one dimensional Schrodinger operators $H_lambda=-frac{d^2}{dx^2}+U+ lambda V_lambda$ with a nonlinear dependence on parameter $lambda$ and study the small $lambda$ behaviour of eigenvalues. Potentials $U$ and $V_lambda$ are real-valued bounded functions of compact support. Under some assumptions on $U$ and $V_lambda$, we prove the existence of a negative eigenvalue that is absorbed at the bottom of the continuous spectrum as $lambdato 0$. We also construct two-term asymptotic formulas for the threshold eigenvalues.
{"title":"Eigenvalues of Schrödinger operators near thresholds: two term approximation","authors":"Yuriy Golovaty","doi":"10.31392/MFAT-npu26_1.2020.06","DOIUrl":"https://doi.org/10.31392/MFAT-npu26_1.2020.06","url":null,"abstract":"We consider one dimensional Schrodinger operators $H_lambda=-frac{d^2}{dx^2}+U+ lambda V_lambda$ with a nonlinear dependence on parameter $lambda$ and study the small $lambda$ behaviour of eigenvalues. Potentials $U$ and $V_lambda$ are real-valued bounded functions of compact support. Under some assumptions on $U$ and $V_lambda$, we prove the existence of a negative eigenvalue that is absorbed at the bottom of the continuous spectrum as $lambdato 0$. We also construct two-term asymptotic formulas for the threshold eigenvalues.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42462366","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 : 2018-08-24DOI: 10.31392/mfat-npu26_3.2021.02
N. Athmouni, Mondher Damak, C. Jendoubi
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for such spectra.
{"title":"On the ascent-descent spectrum","authors":"N. Athmouni, Mondher Damak, C. Jendoubi","doi":"10.31392/mfat-npu26_3.2021.02","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2021.02","url":null,"abstract":"We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for such spectra.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44128537","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 : 2018-04-23DOI: 10.31392/MFAT-npu26_1.2020.05
K. Eftekharinasab
We provide sufficient conditions for the existence of a global diffeomorphism between tame Fr'echet spaces. We prove a version of Mountain Pass theorem which plays a key ingredient in the proof of the main theorem.
{"title":"On the existence of a global diffeomorphism between Fréchet spaces","authors":"K. Eftekharinasab","doi":"10.31392/MFAT-npu26_1.2020.05","DOIUrl":"https://doi.org/10.31392/MFAT-npu26_1.2020.05","url":null,"abstract":"We provide sufficient conditions for the existence of a global diffeomorphism between tame Fr'echet spaces. We prove a version of Mountain Pass theorem which plays a key ingredient in the proof of the main theorem.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46148559","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}
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