Functional Equations: History, Applications and Theory

1. Front Matter

   Pages i-ix

   PDF

2. Essays

   1. Front Matter

      Pages 1-1

      PDF

   2. On history, applications and theory of functional equations

      • J. Aczél

      Pages 3-12

   3. The esthetics and usefulness of functional equations

      • Cl. Alsina

      Pages 13-15

   4. On the historical role of functional equations

      • J. G. Dhombres

      Pages 17-31

   5. Functional equation methods applied to economic problems: some examples

      • W. Gehrig

      Pages 33-52

   6. On multiple uses of some classical equations

      • L. Reich

      Pages 53-54

   7. On some unexpected theoretical and practical applications of functional equations

      • A. Sklar

      Pages 55-56

   8. Functional equations on groupoids and related structures

      • A. Krapež

      Pages 57-64

3. Papers

   1. Front Matter

      Pages 65-65

      PDF

   2. Some recent applications of functional equations

      • J. G. Dhombres

      Pages 67-91

   3. Groupoids with Δ-kernels

      • A. Krapež

      Pages 93-97

   4. The regularity of solutions of functional equations and hypoellipticity

      • A. Tsutsumi, Sh. Haruki

      Pages 99-112

   5. An improvement of the Nevanlinna-Pólya theorem

      • H. Haruki

      Pages 113-126

   6. On polynomials in additive and multiplicative functions

      • L. Reich, J. Schwaiger

      Pages 127-160

   7. Truncations of distribution functions

      • Cl. Alsina

      Pages 161-165

   8. Kurepa’s functional equation on Gaussian semigroups

      • B. R. Ebanks

      Pages 167-173

   9. Some recent results on information measures, a new generalization and some ‘real life’ interpretations of the ‘old’ and new measures

      • J. Aczél

      Pages 175-189

   10. On a characterization of the Shannon concentration measure

       • W. Gehrig

       Pages 191-205

   11. Closed invariant curves of a noncontinuously dififerentiable recurrence

       • R. Thibault

       Pages 207-215

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 mathe­ matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) ~n re­ 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 pro­ gramming profit from homotopy theory; Lie algebras are rele­ 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.

• distribution
• filtering
• functional equation
• integrable system
• measure
• measure theory

• Centre for Information Theory, University of Waterloo, Canada

  J. Aczél

Policies and ethics