LEADER 04661nam 22006495 450 001 9910438152603321 005 20200706145933.0 010 $a1-283-93462-0 010 $a3-0348-0294-3 024 7 $a10.1007/978-3-0348-0294-9 035 $a(CKB)3400000000101268 035 $a(EBL)1082161 035 $a(OCoLC)823728855 035 $a(SSID)ssj0000879921 035 $a(PQKBManifestationID)11454609 035 $a(PQKBTitleCode)TC0000879921 035 $a(PQKBWorkID)10872152 035 $a(PQKB)10090643 035 $a(DE-He213)978-3-0348-0294-9 035 $a(MiAaPQ)EBC1082161 035 $a(PPN)168307022 035 $a(EXLCZ)993400000000101268 100 $a20121212d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Weyl Operator and its Generalization$b[electronic resource] /$fby Leon Cohen 205 $a1st ed. 2013. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (166 p.) 225 1 $aPseudo-Differential Operators, Theory and Applications,$x2297-0355 300 $aDescription based upon print version of record. 311 $a3-0348-0293-5 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- The Fundamental Idea, Terminology, and Operator Algebra -- The Weyl Operator -- The Algebra of the Weyl Operator -- Product of Operators, Commutators, and the Moyal Sin Bracket -- Some Other Ordering Rules -- Generalized Operator Association -- The Fourier, Monomial, and Delta Function Associations -- Transformation Between Associations -- Path Integral Approach -- The Distribution of a Symbol and Operator -- The Uncertainty Principle -- Phase-Space Distributions -- Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform -- Time - Frequency Analysis -- The Transformation of Differential Equations into Phase Space -- The Representation of Functions -- The N Operator Case. 330 $aThis book deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areas of science and mathematics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generally being the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that do not commute. Methods to do so became known as rules of association, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it was realized that for every correspondence rule there is a corresponding phase-space distribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the field of time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Operator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner. 410 0$aPseudo-Differential Operators, Theory and Applications,$x2297-0355 606 $aPartial differential equations 606 $aOperator theory 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aPartial differential equations. 615 0$aOperator theory. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aOperator Theory. 615 24$aMathematical Physics. 676 $a530.15 700 $aCohen$b Leon$4aut$4http://id.loc.gov/vocabulary/relators/aut$027774 906 $aBOOK 912 $a9910438152603321 996 $aThe Weyl Operator and its Generalization$92513623 997 $aUNINA