{"id":1946,"date":"2014-05-15T12:12:06","date_gmt":"2014-05-15T07:12:06","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?page_id=1946"},"modified":"2016-11-15T13:09:42","modified_gmt":"2016-11-15T09:09:42","slug":"department-of-non-harmonic-analysis","status":"publish","type":"page","link":"https:\/\/www.imm.az\/exp\/departments\/department-of-non-harmonic-analysis\/","title":{"rendered":"Department of “Non-harmonic analysis”"},"content":{"rendered":"

\"Qeyri_harmonik_analiz\"<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Head of the department:<\/strong><\/td>\nProf. Bilal Bilalov
\nCorrespondent member of ANAS,\u00a0Doctor of Sciences in Physics and Mathematics<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
Tel:<\/strong><\/td>\n(+994 12)\u00a0 5387250<\/td>\n<\/tr>\n
E-mail:<\/strong><\/td>\n\u00a0bilal.bilalov@imm.az<\/a>\u00a0,\u00a0bilalov.bilal@gmail.com<\/a><\/td>\n<\/tr>\n
Number of employees:<\/strong><\/td>\n24<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
Main Research Areas:<\/strong><\/td>\nNon-harmonic Fourier series; bases problems in linear topological spaces; basis properties of exponential systems in functional spaces; spectral properties of ordinary discrete\u00a0 differential operators; frame theory-wavelet analysis and applications; financial (risk or actuary) mathematics, pattern recognition<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
Main Scientific Results:<\/strong><\/td>\n\n
    \n
  • Kostyuchenko problem from the spectral theory of differential operators is completely solved;<\/li>\n
  • classical Paley-Wiener and Bari theorems on bases are generalized with respect to the systems of elements\u00a0 and the systems of subspaces;<\/li>\n
  • basicity criterion (Riesz basicity in the Hilbert case) for trigonometric systems in Lebesgue spaces with some asymptotics is found; the concept of\u00a0 \u201cb-basis\u201d generated by some bilinear mapping which generalizes Schauder basis is introduced, classical facts about the theory of bases are extended to this case;<\/li>\n
  • major results on basicity for the systems with infinite defect in subspaces of Banach spaces are obtained;<\/li>\n
  • some Banach analogues of the Lax-Milgram theorem are proved;<\/li>\n
  • some complex analogues of well-known Stone-Weierstrass theorem\u00a0 are proved and extended to the case of the space of piecewise continuous functions;<\/li>\n
  • basis properties of linear phase trigonometric systems are studied in generalized Lebesgue spaces;<\/li>\n
  • important results are obtained on basicity, equiconvergence, uniform and absolute convergence of series with respect to eigenfunctions and associated functions of differential operators;<\/li>\n
  • a classification of solutions of abstract differential equations with discontinuous coefficients in weighted Sobolev spaces is given, existence and uniqueness of solutions are proved;<\/li>\n
  • the concept of the regularity of the boundary conditions for discontinuous differential operators \u00a0is introduced \u00a0and the theorems \u00a0on a basicity \u00a0of the system of eigenfunctions and associated functions of a regular boundary value problems are proved;<\/li>\n
  • the results are obtained from the description of areas of fractional powers of discontinuous differential operators, for the study of basis properties of spectral problems containing the spectral parameter in the boundary conditions, in the spaces Lp + Cm<\/sup> and Lp abstract theorems are proved and\u00a0 their application are given;<\/li>\n
  • a new method for obtaining\u00a0 the bases in the direct sum of Banach spaces is introduced and their applications are given;<\/li>\n
  • basicity criterion in \u00a0for trigonometric systems with polynomial type phase is found. Basis properties of trigonometric type systems are studied in a Banach space of piecewise continuous functions;<\/li>\n
  • an abstract analogue of the Riemann problem is considered, Noetherness of this problem is studied and the obtained results are applied to basis-related problems.;<\/li>\n
  • the basicity of eigenfunctions of some discontinuous differential operator in Lebesgue spaces is studied;<\/li>\n
  • Some analogues of the well-known Kadets \u00bc-theorem with respect to the systems of exponent, cosines, sines\u00a0 and some abstract analogues are obtained;<\/li>\n
  • abstract analogues of classical systems of power, sines and cosines are introduced,\u00a0 a relationship between their basis\u00a0 properties in Banach spaces is found;<\/li>\n
  • space of coefficients\u00a0 generated by non-degenerate systems, transferred to different mathematical structures,\u00a0 the generalizations of the theory of analytic functions\u00a0 is given generated by\u00a0 nilpotent and idempotent operators, the concept of corresponding bases is introduced;<\/li>\n
  • basis properties \u00a0\u00a0of double systems consisting of generalized Faber polynomials with complex coefficients on Carleson curve is studied in Lebesgue spaces;<\/li>\n
  • Noetherness\u00a0\u00a0 perturbation of Hilbert and Banach frames is studied, the concept of t-frame generated by the Hilbert tensor product is introduced, and its\u00a0\u00a0 Noetherness\u00a0\u00a0 perturbation is studied; the basiscity\u00a0 of the classical exponential systems in Morrey type spaces is proved;<\/li>\n
  • the basis properties of\u00a0 perturbed trigonometric\u00a0\u00a0 systems in weighted generalized Lebesgue spaces are studied;<\/li>\n
  • the notion of statistical convergence\u00a0 is transferred\u00a0 to the\u00a0\u00a0 different mathematical structures,\u00a0 the notion of \u03bc-statistical convergence and \u03bc-statistical\u00a0 fundamentality\u00a0 at the\u00a0 point in a measurable space are introduced and their equivalence is proved;<\/li>\n
  • the notion of \u03bc-statistical limits, \u03bc-statistical completeness, \u03bc-statistical fundamentality, \u03bc-statistical equivalence of functions, \u03bc-statistical continuity at infinity are introduced and some properties are studied;<\/li>\n
  • the basis\u00a0 properties of trigonometric perturbed systems in\u00a0 generalized and weighted generalized Lebesgue spaces are studied;<\/li>\n
  • signals of solar radiation (total, diffuse and reflected) are\u00a0 processed by wavelet analysis.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

    Head of the department: Prof. Bilal Bilalov Correspondent member of ANAS,\u00a0Doctor of Sciences in Physics and Mathematics Tel: (+994 12)\u00a0 5387250 E-mail: \u00a0bilal.bilalov@imm.az\u00a0,\u00a0bilalov.bilal@gmail.com Number of employees: 24 Main Research Areas: Non-harmonic Fourier series; bases problems in linear topological spaces; basis properties of exponential systems in functional spaces; spectral properties of ordinary discrete\u00a0 differential operators; frame […]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":1913,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/1946"}],"collection":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/comments?post=1946"}],"version-history":[{"count":5,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/1946\/revisions"}],"predecessor-version":[{"id":9440,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/1946\/revisions\/9440"}],"up":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/1913"}],"wp:attachment":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media?parent=1946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}