Methods of Functional Analysis
and Topology

Editors-in-Chief: A. N. Kochubei, Yu. G. Kondratiev
ISSN: 1029-3531 (Print) 2415-7503 (Online)

Founded by Yu. M. Berezansky in 1995.

Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.

MFAT is an open access journal, free for authors and free for readers.

MFAT is indexed in: MathSciNet, zbMATH, Scopus, Web of Science, DOAJ, Google Scholar

Volumes: 25 | Issues: 95 | Articles: 735 | Authors: 541

Latest Articles (September, 2019)

The Fourier transform on 2-step Lie groups

Guillaume Lévy

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 25 (2019), no. 3, 248-272

In this paper, we study the Fourier transform on finite dimensional $2$-step Lie groups in terms of its canonical bilinear form (CBF) and its matrix coefficients. The parameter space of these matrix coefficients $\tilde{g}$, endowed with a distance $\rho_E$ which exchanges the regularity of a function with the decay of its Fourier matrix coefficients (cf. the Riemann-Lebesgue lemma for the classical Fourier transform) is however not complete. We compute explicitly its completion $\hat{g}$; the lack of completeness appears exactly when the CBF has nonmaximal rank. We provide an example for which partial degeneracy (partial rank loss) of the canonical form occurs, as opposed to the full degeneracy at the origin. We also compute the kernel $(w,\hat{w}) \mapsto \Theta(w,\hat{w})$ of the matrix-coefficients Fourier transform, the analogue for the $2$-step groups of the classical Fourier kernel $(x,\xi) \mapsto e^{i \langle \xi, x\rangle}$.

Problem of determining a multidimensional thermal memory in a heat conductivity equation

D. K. Durdiev, Zh. Zh. Zhumayev

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 25 (2019), no. 3, 219-226

We consider a multidimensional integro-differential equation of heat conductivity with time-convolution integral in the right hand-side. The direct problem is represented by the Cauchy problem of determining the temperature of the medium for a known initial distribution of heat. We study the inverse problem of determining the kernel, in the integral part, that depends on time and spatial variables, if a solution of the direct problem is known on the hyperplane $x_n=0$ for $t>0.$ With a use of the resolvent of the kernel, this problem is reduced to a study of a more convenient inverse problem. The later problem is replaced with an equivalent system of integral equations with respect to the unknown functions and, using a contractive mapping, we prove that the direct and the inverse problems have unique solutions.

Anatoly Naumovich Kochubei (to 70th birthday anniversary)

Editorial Board

Article (.pdf)

Methods Funct. Anal. Topology 25 (2019), no. 3, 195-196

On the $F$-contraction properties of multivalued integral type transformations

Derya Sekman, Vatan Karakaya

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 25 (2019), no. 3, 282-288

The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under $F$-contraction. In addition, the results of this study were evaluated with some interesting example.

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