國立虎尾科技大學 |

Convolution-like Structures, Differential Operators and Diffusion Processes

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Convolution-like Structures, Differential Operators and Diffusion Processes/ by Rúben Sousa, Manuel Guerra, Semyon Yakubovich.
作者:	Sousa, Rúben.
其他作者:	Yakubovich, Semyon.
面頁冊數:	XII, 262 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Integral Transforms and Operational Calculus. -
電子資源:	https://doi.org/10.1007/978-3-031-05296-5
ISBN:	9783031052965

Convolution-like Structures, Differential Operators and Diffusion Processes
Sousa, Rúben.

Convolution-like Structures, Differential Operators and Diffusion Processes[electronic resource] /by Rúben Sousa, Manuel Guerra, Semyon Yakubovich. - 1st ed. 2022. - XII, 262 p. 1 illus. in color.online resource. - Lecture Notes in Mathematics,23151617-9692 ;. - Lecture Notes in Mathematics,2144.

This book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

ISBN: 9783031052965

Standard No.: 10.1007/978-3-031-05296-5doiSubjects--Topical Terms:

1366597
Integral Transforms and Operational Calculus.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Convolution-like Structures, Differential Operators and Diffusion Processes
LDR:02668nam a22004215i 4500 001 1089101
003 DE-He213
005 20220727210908.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031052965 $9 978-3-031-05296-5
024 7 $a 10.1007/978-3-031-05296-5 $2 doi
035 $a 978-3-031-05296-5
050 4 $a QA273.A1-274.9
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Sousa, Rúben. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396341
245 1 0 $a Convolution-like Structures, Differential Operators and Diffusion Processes $h [electronic resource] / $c by Rúben Sousa, Manuel Guerra, Semyon Yakubovich.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XII, 262 p. 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes in Mathematics, $x 1617-9692 ; $v 2315
520 $a This book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.
650 2 4 $a Integral Transforms and Operational Calculus. $3 1366597
650 2 4 $a Special Functions. $3 672152
650 2 4 $a Operator Theory. $3 672127
650 1 4 $a Probability Theory. $3 1366244
650 0 $a Mathematical analysis. $3 527926
650 0 $a Special functions. $3 1257411
650 0 $a Operator theory. $3 527910
650 0 $a Probabilities. $3 527847
700 1 $a Yakubovich, Semyon. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396343
700 1 $a Guerra, Manuel. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396342
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031052958
776 0 8 $i Printed edition: $z 9783031052972
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2144 $3 1254300
856 4 0 $u https://doi.org/10.1007/978-3-031-05296-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)