000 03883nam a22004695i 4500
001 978-3-0348-0294-9
003 DE-He213
005 20140220082836.0
007 cr nn 008mamaa
008 121212s2013 sz | s |||| 0|eng d
020 _a9783034802949
_9978-3-0348-0294-9
024 7 _a10.1007/978-3-0348-0294-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aCohen, Leon.
_eauthor.
245 1 4 _aThe Weyl Operator and its Generalization
_h[electronic resource] /
_cby Leon Cohen.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aXII, 159 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aPseudo-Differential Operators, Theory and Applications ;
_v9
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aOperator theory.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aOperator Theory.
650 2 4 _aMathematical Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034802932
830 0 _aPseudo-Differential Operators, Theory and Applications ;
_v9
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0294-9
912 _aZDB-2-SMA
999 _c96283
_d96283