國立虎尾科技大學 |

Combined Measure and Shift Invariance Theory of Time Scales and Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Combined Measure and Shift Invariance Theory of Time Scales and Applications/ by Chao Wang, Ravi P. Agarwal.
作者:	Wang, Chao.
其他作者:	Agarwal, Ravi P.
面頁冊數:	XVI, 434 p. 2 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Real Functions. -
電子資源:	https://doi.org/10.1007/978-3-031-11619-3
ISBN:	9783031116193

Combined Measure and Shift Invariance Theory of Time Scales and Applications
Wang, Chao.

Combined Measure and Shift Invariance Theory of Time Scales and Applications[electronic resource] /by Chao Wang, Ravi P. Agarwal. - 1st ed. 2022. - XVI, 434 p. 2 illus.online resource. - Developments in Mathematics,772197-795X ;. - Developments in Mathematics,41.

Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales -- ♢α-Measurability and Combined Measure Theory on Time Scales -- Shift Invariance and Matched Spaces of Time Scales -- Almost Periodic Functions under Matched Spaces of Time Scales -- Almost Automorphic Functions under Matched Spaces of Time Scales -- C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales -- Almost Periodic Dynamic Equations under Matched Spaces -- Almost Automorphic Dynamic Equations under Matched Spaces -- Applications on Dynamics Models under Matched Spaces.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.

ISBN: 9783031116193

Standard No.: 10.1007/978-3-031-11619-3doiSubjects--Topical Terms:

672094
Real Functions.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Combined Measure and Shift Invariance Theory of Time Scales and Applications
LDR:03666nam a22004095i 4500 001 1083438
003 DE-He213
005 20220924065725.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031116193 $9 978-3-031-11619-3
024 7 $a 10.1007/978-3-031-11619-3 $2 doi
035 $a 978-3-031-11619-3
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Wang, Chao. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1209253
245 1 0 $a Combined Measure and Shift Invariance Theory of Time Scales and Applications $h [electronic resource] / $c by Chao Wang, Ravi P. Agarwal.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XVI, 434 p. 2 illus. $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 Developments in Mathematics, $x 2197-795X ; $v 77
505 0 $a Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales -- ♢α-Measurability and Combined Measure Theory on Time Scales -- Shift Invariance and Matched Spaces of Time Scales -- Almost Periodic Functions under Matched Spaces of Time Scales -- Almost Automorphic Functions under Matched Spaces of Time Scales -- C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales -- Almost Periodic Dynamic Equations under Matched Spaces -- Almost Automorphic Dynamic Equations under Matched Spaces -- Applications on Dynamics Models under Matched Spaces.
520 $a This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
650 2 4 $a Real Functions. $3 672094
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Differential Equations. $3 681826
650 1 4 $a Functional Analysis. $3 672166
650 0 $a Functions of real variables. $3 792248
650 0 $a Measure theory. $3 527848
650 0 $a Differential equations. $3 527664
650 0 $a Functional analysis. $3 527706
700 1 $a Agarwal, Ravi P. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 684508
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031116186
776 0 8 $i Printed edition: $z 9783031116209
776 0 8 $i Printed edition: $z 9783031116216
830 0 $a Developments in Mathematics, $x 1389-2177 ; $v 41 $3 1256322
856 4 0 $u https://doi.org/10.1007/978-3-031-11619-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)