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πŸ“

Functional Equations: History, Applications and Theory

✍ Scribed by J. Aczél (auth.)


Publisher
Springer Netherlands
Year
1984
Tongue
English
Leaves
242
Series
Mathematics and Its Applications 12
Edition
1
Category
Library

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✦ Synopsis


Approach your problems from It isn't that they can't see the right end and begin with the solution. It is that they the answers. Then one day, can't see the problem. perhaps you will find the G.K. Chesterton. The Scandal of final question. Father Brown 'The Point of a Pin' . 'The Hermit Clad ~n Crane Feathers' in R. van Gulik's The Chinese Haze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of matheΒ­ matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) ~n reΒ­ gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical proΒ­ gramming profit from homotopy theory; Lie algebras are releΒ­ vant to filtering; and prediction and electrical en~ineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existinf, classifi~ation schemes. They draw upon widely different sections of mathematics.

✦ Table of Contents


Front Matter....Pages i-ix
Front Matter....Pages 1-1
On history, applications and theory of functional equations....Pages 3-12
The esthetics and usefulness of functional equations....Pages 13-15
On the historical role of functional equations....Pages 17-31
Functional equation methods applied to economic problems: some examples....Pages 33-52
On multiple uses of some classical equations....Pages 53-54
On some unexpected theoretical and practical applications of functional equations....Pages 55-56
Functional equations on groupoids and related structures....Pages 57-64
Front Matter....Pages 65-65
Some recent applications of functional equations....Pages 67-91
Groupoids with Ξ”-kernels....Pages 93-97
The regularity of solutions of functional equations and hypoellipticity....Pages 99-112
An improvement of the Nevanlinna-PΓ³lya theorem....Pages 113-126
On polynomials in additive and multiplicative functions....Pages 127-160
Truncations of distribution functions....Pages 161-165
Kurepa’s functional equation on Gaussian semigroups....Pages 167-173
Some recent results on information measures, a new generalization and some β€˜real life’ interpretations of the β€˜old’ and new measures....Pages 175-189
On a characterization of the Shannon concentration measure....Pages 191-205
Closed invariant curves of a noncontinuously dififerentiable recurrence....Pages 207-215
Invariant curves as solutions of functional equations....Pages 217-226
The cycle theorem for flows....Pages 227-229
Back Matter....Pages 231-245

✦ Subjects


Analysis


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