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Asekritova, Irina
Publications (10 of 15) Show all publications
Asekritova, I., Cobos, F. & Kruglyak, N. (2015). Interpolation of Closed Subspaces and Invertibility of Operators. Journal of Analysis and its Applications, 34(2015), 1-15
Open this publication in new window or tab >>Interpolation of Closed Subspaces and Invertibility of Operators
2015 (English)In: Journal of Analysis and its Applications, ISSN 0232-2064, Vol. 34, no 2015, p. 1-15Article in journal (Refereed) Published
Abstract [en]

Let (Y0,Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj, (j = 0,1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0,X1)θ,q is a closed subspace of (Y0,Y1)θ,q. In particular, we establish conditions which are necessary and sufficient for the equality (X0,X1)θ,q = (Y0,Y1)θ,q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0. 

Keywords
Interpolation of subspaces, K-functional, Sobolev spaces.
National Category
Geometry
Identifiers
urn:nbn:se:liu:diva-114623 (URN)10.4171/ZAA/1525 (DOI)000355126600001 ()
Available from: 2015-02-28 Created: 2015-02-28 Last updated: 2015-06-22
Asekritova, I. & Kruglyak, N. (2013). Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation. Journal of Functional Analysis, 264(1), 207-245
Open this publication in new window or tab >>Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation
2013 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, no 1, p. 207-245Article in journal (Refereed) Published
Abstract [en]

Let A be a bounded linear operator from a couple (X-0, X-1) to a couple (Y-0, Y-1) such that the restrictions of A on the end spaces X-0 and X-1 have bounded inverses defined on Y-0 and Y-1, respectively. We are interested in the problem of how to determine if the restriction of A on the space (X-0, XI)(theta,q) has a bounded inverse defined on the space (Y-0, Y-1)(theta,q). In this paper, we show that a solution to this problem can be given in terms of indices of two subspaces of the kernel of the operator A on the space X-0 + X-1.

Place, publisher, year, edition, pages
Elsevier, 2013
Keywords
Real interpolation, Invertibility of operators
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-87240 (URN)10.1016/j.jfa.2012.10.007 (DOI)000312115100008 ()
Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2017-12-06
Asekritova, I. & Kruglyak, N. (2010). The Besicovitch covering theorem and near-minimizers for the couple (L-2, BV). Proceedings of the Estonian Academy of Sciences, 59(1), 29-33
Open this publication in new window or tab >>The Besicovitch covering theorem and near-minimizers for the couple (L-2, BV)
2010 (English)In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 1, p. 29-33Article in journal (Refereed) Published
Abstract [en]

Let Omega be a rectangle in R-2. A new algorithm for the construction of a near-minimizer for the couple (L-2 (Omega); BV(Omega)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f is an element of L-2 (Omega).

Place, publisher, year, edition, pages
Estonian Academy Publishers, 2010
Keywords
covering theorems, near-minimizers
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:liu:diva-56295 (URN)10.3176/proc.2010.1.05 (DOI)000276989900005 ()
Available from: 2010-05-07 Created: 2010-05-07 Last updated: 2017-12-12
Asekritova, I. & Kruglyak, N. (2010). The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV). Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, 59(1), 29-33
Open this publication in new window or tab >>The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV)
2010 (English)In: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 59, no 1, p. 29-33Article in journal (Refereed) Published
Abstract [en]

Let Ω be a rectangle in R2. A new algorithm for the construction of a near-minimizer for the couple (L2(Ω), BV(Ω)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f ∈ L2(Ω).

Keywords
real interpolation, Besicovitch Covering Theorem, near minimizers
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:liu:diva-106174 (URN)10.3176/proc.2010.1.05 (DOI)
Available from: 2010-08-22 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved
Asekritova, I., Nilsson, B. & Rydström, S. (2009). Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data. In: Nilsson B. (Ed.), Mathematical modeling of wave phenomena: . Paper presented at 3rd Conference on Mathematical Modeling of Wave phenomena, 20th Nordic Conference on Radio Science and Communication, Växjö, Sweden, 13-19 June 2008 (pp. 224-232). American Institute of Physics (AIP)
Open this publication in new window or tab >>Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
2009 (English)In: Mathematical modeling of wave phenomena, American Institute of Physics (AIP), 2009, p. 224-232Conference paper, Published paper (Other academic)
Abstract [en]

Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2009
Series
AIP Conference Proceedings, ISSN 0094-243X ; 1106
Keywords
string vibrations, Tikhonov regularization, elastic properties, inverse problem
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-90403 (URN)10.1063/1.3117098 (DOI)978-0-7354-0643-8 (ISBN)
Conference
3rd Conference on Mathematical Modeling of Wave phenomena, 20th Nordic Conference on Radio Science and Communication, Växjö, Sweden, 13-19 June 2008
Available from: 2013-03-25 Created: 2013-03-25 Last updated: 2014-04-28
Asekritova, I. & Kruglyak, N. (2008). Invertibility of Operators in Spaces of Real Interpolation. Revista Matemática Complutense, 21(1), 207-217
Open this publication in new window or tab >>Invertibility of Operators in Spaces of Real Interpolation
2008 (English)In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 21, no 1, p. 207-217Article in journal (Refereed) Published
Abstract [en]

Let be a linear bounded operator from a couple to a couple such that the restrictions of on the spaces and have bounded inverses. This condition does not imply that the restriction of on the real interpolation space has a bounded inverse for all values of the parameters and . In this paper under some conditions on the kernel of we describe all spaces such that the operator has a bounded inverse.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-90397 (URN)
Available from: 2013-03-25 Created: 2013-03-25 Last updated: 2013-04-04
Asekritova, I. (2008). Regularization Theory and Real Interpolation. In: : . Paper presented at International Workshop on Interpolation Theory, Function Spaces and Related Topics, September 7-13, Toledo Spain.
Open this publication in new window or tab >>Regularization Theory and Real Interpolation
2008 (English)Conference paper, Oral presentation only (Other academic)
Abstract [en]

In inverse problems we often need to solve numerically unstable problems that are very sensitive to noise. One of the approaches to such type of problems is classical regularization theory for Hilbert spaces. In the talk I plan to show connections between this theory and the theory of real interpolation, give di®erent examples and discuss a non - Hilbert case - the couple (L2;BV ).

National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:liu:diva-106180 (URN)
Conference
International Workshop on Interpolation Theory, Function Spaces and Related Topics, September 7-13, Toledo Spain
Available from: 2009-01-07 Created: 2014-04-28 Last updated: 2014-04-28Bibliographically approved
Asekritova, I. & Kruglyak, N. (2007). Interpolation of Besov Spaces in the Non-Diagonal Case. St. Petersburg Mathematical Journal, 18(4), 511-516
Open this publication in new window or tab >>Interpolation of Besov Spaces in the Non-Diagonal Case
2007 (English)In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 18, no 4, p. 511-516Article in journal (Refereed) Published
Abstract [en]

In the nondiagonal case, interpolation spaces for a collection of Besov spaces are described. The results are consequences of the fact that, whenever the convex hull of points includes a ball of , we have where

and

.

National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:liu:diva-106179 (URN)
Available from: 2007-03-14 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved
Asekritova, I. (2006). Interpolation of Approximation Spaces with Nonlinear Projectors. Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, 55(3), 146-149
Open this publication in new window or tab >>Interpolation of Approximation Spaces with Nonlinear Projectors
2006 (English)In: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 55, no 3, p. 146-149Article in journal (Refereed) Published
Abstract [en]

Approximation spaces defined by multiparametric approximation families with possible nonlinear projectors are considered. It is shown that a real interpolation space for a tuple of such spaces is again an approximation space of the same type.

Keywords
interpolation functor, approximation space, K-functional
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:liu:diva-106178 (URN)
Available from: 2007-03-14 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved
Asekritova, I., Kruglyak, N. & Nikolova, L. (2005). Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation. Studia Mathematica, 170(3), 227-239
Open this publication in new window or tab >>Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
2005 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 170, no 3, p. 227-239Article in journal (Refereed) Published
Abstract [en]

A complete description of the real interpolation space L=(Lp0(ω0),…,Lpn(ωn))θ⃗ ,q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ωi (i∈I) such that L is an lq sum of the restrictions of L to Ωi, and L on each Ωi is a result of interpolation of just two weighted Lp spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.

Keywords
Real interpolation, Lizorkin-Freitag formula, vector-valued spaces
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:liu:diva-106169 (URN)10.4064/sm170-3-2 (DOI)
Available from: 2010-08-22 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved
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