Extensions of Positive Definite Functions: Applications and Their Harmonic Analysis: 2160 (Lecture Notes in Mathematics) - Softcover

Jorgensen, Palle; Pedersen, Steen; Tian, Feng

Softcover

ISBN 10: 3319397796 ISBN 13: 9783319397795

Verlag: Springer, 2016

Inhaltsangabe

<DIV>THIS MONOGRAPH DEALS WITH THE MATHEMATICS OF EXTENDING GIVEN PARTIAL DATA-SETS OBTAINED FROM EXPERIMENTS;&NBSP;</DIV><DIV>EXPERIMENTALISTS FREQUENTLY GATHER SPECTRAL DATA WHEN THE OBSERVED DATA IS LIMITED, E.G., BY THE PRECISION OF INSTRUMENTS; OR BY OTHER LIMITING EXTERNAL FACTORS. HERE&NBSP;THE LIMITED INFORMATION IS A RESTRICTION, AND THE EXTENSIONS TAKE THE FORM OF FULL POSITIVE DEFINITE FUNCTION ON SOME PRESCRIBED GROUP.&NBSP;IT IS THEREFORE BOTH AN ART AND A SCIENCE TO PRODUCE SOLID CONCLUSIONS FROM RESTRICTED OR LIMITED DATA.&NBSP;</DIV><DIV><BR></DIV><DIV>WHILE THE THEORY OF IS IMPORTANT IN MANY AREAS OF PURE AND APPLIED MATHEMATICS, IT IS DIFFICULT FOR STUDENTS AND FOR THE NOVICE TO THE FIELD, TO FIND ACCESSIBLE PRESENTATIONS WHICH COVER ALL RELEVANT POINTS OF VIEW, AS WELL AS STRESSING COMMON IDEAS AND INTERCONNECTIONS. WE HAVE AIMED AT FILLING THIS GAP, AND WE HAVE STRESSED HANDS-ON-EXAMPLES.</DIV>

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Reseña del editor:

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. 
While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

Über diese Auflage

• Verlag: Springer
• Erscheinungsdatum: 2016
• ISBN 10: 3319397796
• ISBN 13: 9783319397795
• Einband: Tapa blanda
• Auflage: 1
• Anzahl der Seiten: 260