GENERALIZED SPACES OF S AND S′ TYPES
Keywords:
the space of generalized function, Fourier transformation, pseudodifferential operator, well-posed solvability, the Cauchy problem, multiplier, convolution, convolutor
Abstract
In paper the topological structure of generalized spaces of $ S $ type and the basic operations in such spaces was investigated. The question of quasi-analyticity (non-quasi-analyticity) of generalized spaces of $ S $ type was studied. Some classes of pseudodifferential operators, properties of Fourier transformation of generalized functions from spaces of type $S'$, convolutions, convoluters and multipliers was investigated.
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References
References
[1] Gelfand I.M., Shilov G.E. Spaces of main and generalized functions. M., Fizmatgiz, 1958. 307 p.
[2] M.L. Gorbachuk and P.I. Dudnikov. On the initial data of the Cauchy problem for parabolic equations for which the solutions are infinitely differentiable. Dokl. USSR Academy of Sciences. Ser. A., 1981, No 4. 9–11.
[3] Gorbachuk V.I., Gorbachuk M.L. Boundary value problems for differential-operator equations. Kiev, Science. opinion, 1984. 284 p.
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[6] Horodetskiy V.V. Evolutionary equations in countable-normalized spaces of infinitely differentiable functions. Chernivtsi, Ruta, 2008. 400 p.
[7] Mandelbroit S. Quasi-analytic classes of functions. M., Gostehizdat, 1937. 156 p.
[8] Horodetskiy V.V., Nagnibida N.I., Nastasiev P.P. Methods for solving problems in functional analysis. Kiev, Higher School, 1990. 479 p.
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[1] Gelfand I.M., Shilov G.E. Spaces of main and generalized functions. M., Fizmatgiz, 1958. 307 p.
[2] M.L. Gorbachuk and P.I. Dudnikov. On the initial data of the Cauchy problem for parabolic equations for which the solutions are infinitely differentiable. Dokl. USSR Academy of Sciences. Ser. A., 1981, No 4. 9–11.
[3] Gorbachuk V.I., Gorbachuk M.L. Boundary value problems for differential-operator equations. Kiev, Science. opinion, 1984. 284 p.
[4] Horodetskiy V.V. Boundary properties of solutions of equations of parabolic type smooth in a layer. Chernivtsi, Ruta, 1998. 225 p.
[5] Horodetskiy V.V. Sets of initial values of smooth solutions of differential-operator equations of parabolic type. Chernivtsi, Ruta, 1998. 219 p.
[6] Horodetskiy V.V. Evolutionary equations in countable-normalized spaces of infinitely differentiable functions. Chernivtsi, Ruta, 2008. 400 p.
[7] Mandelbroit S. Quasi-analytic classes of functions. M., Gostehizdat, 1937. 156 p.
[8] Horodetskiy V.V., Nagnibida N.I., Nastasiev P.P. Methods for solving problems in functional analysis. Kiev, Higher School, 1990. 479 p.
[9] Gelfand I.M., Shilov G.E. Fourier transform of fast-growing functions and Fourier integrals. Uspekhi Mat. Science, 1951, 6, iss. 2. 102–143.
[10] Horodetskiy V.V., Drin Y.M., Nagnibida M.I. Generalized functions. Methods of solving problems. Chernivtsi, Books – XXI, 2011. 504 p.
Published
2023-09-28
How to Cite
[1]
Gorodetskiy, V., Kolisnyk, R. and Shevchuk, N. 2023. GENERALIZED SPACES OF S AND S′ TYPES. Bukovinian Mathematical Journal. 11, 1 (Sep. 2023), 7-25. DOI:https://doi.org/10.31861/bmj2023.01.01.
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