Professor Emeritus and Adjunct Professor

Contact information

Department of Pure Mathematics John A. Baker
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1

Email: jabaker@uwaterloo.ca

BA, MA (Saskatchewan), PhD (Waterloo, 1968),
Sub-Lieutenant RCNR (Ret'd),
Former Occupant of the Bucket Seats of
Classical Analysis and Functional Equations.

Professional research interests and activities

Author of some 55 papers mostly concerned with the following areas:

  • Functional equations from the point of view of classical and modern analysis including distribution theory.
  • Expository writing in calculus and analysis especially concerning connections with other parts of mathematics.

A selection of mathematical papers

Membership in CMS, UNTD Association of Upper Canada and Red Green Fan Club.

Once known as:

  • Watbard among connoisseurs of sensitive verse
  • author of that prophetic document, The Septic System, the essence of a mid 80's unsuccessful campaign for a deanship
  • resident expert on bawdy songs and sea chanties
  • fairly prolific, if sporadic, writer of letters to editors
  • Luddite sympathizer
  • avowed enemy of political correctness

Literary lapses

Other passions and pastimes, past and present: Retired in 1996 - since 1999 - living on 24 acres overlooking Georgian Bay, near the village of Lion's Head, Ontario. Activities include gardening, Bruce Trail maintenance and entertaining (guitar and vocal).

A selection of mathematical papers

Expository articles

  • The Dirichlet Problem for Ellipsoids, Amer. Math. Monthly, 106 (9), (1999), 829-834.
  • Integration Over Spheres and the Divergence Theorem for Balls, American Math. Monthly, 104 (1) (1997), 36-47.
  • Plane Curves, Polar Coordinates and Winding Numbers, Mathematics Magazine, 64, No. 2, 1991, 75-91.
  • A Note on Iterated Integrals, Math. Chronicle 19 (1990), 19-22.

Functional Equations à la Schwartz Distributions

  • Functional Equations, DEs and Distributions, Publ. Math. Debrecen, 48/1-2 (1996), 103-115.

  • Triangular mean value Theorems and Fréchet's equation, Acta Math. Hungar., 69 (1-2) (1995), 111-126.

  • On a Functional Equation of Aczél and Chung, Aequationes Math., 46 (1993), 99-111.

  • Difference Operators, Distrtibutions and Functional Equations, Periodica Mathematica Hungarica, 23(3), 1991, 171-183.

  • Functional Equations, Distributions and Approximate Identities, Can. J. Math. XLII (1990), 696-708.

  • Functional Equations, Tempered Distributions and Fourier Transforms, Trans. Amer. Math. Soc. 315 (1989), 57-68.

The Stability of Functional Equations

  • The Stability of Certain Functional Equations, Proc. Amer. Math. Soc., 112 (3), 1991, 729-732.

  • (with Michael Albert), Functions with Bounded nth Differences, Ann. Polon. Math XLIII (1983), 93-103.

  • The Stability of the Cosine Equation, Proc. Amer. Math. Soc. 80 (1980), 411-416.

Various Analytic Techniques for Functional Equations

  • Mean Value Theorems via Spectral Synthesis, Journal of Mathematical Analysis and Applications, 193 (1995), 306-317.

  • Functional Equations and Weierstrass Transforms, Results in Mathematics, 26 (1994), 199-204.

  • Regularity Properties of Functional Equations, Aequationes Mathematicae 6(2/3) (1971), 243-248.

  • An Analogue of the Wave Equation and Certain Related Functional Equations, Can. Math. Bull. 12(6) (1969), 837-846.

Special Functional Equations

  • A Functional Equation from Probability Theory, Proc. AMS, 121 (No. 3), (1994), 767-773.

  • On Some Mathematical Characters, Glasnik Matematicki, 25(2), 1991, 81-89.

  • (with K. Davidson), Cosine, Exponential and Quadratic Functions, Glasnik Mathematicki 16(36) (1981), 269-274.

  • D'Alembert's Functional Equation in Banach Algebras, Acta. Sci., Math Szeged 32(3-4) (1971), 225-234.

Literary lapses

The Quadruple E Senate

Canada's contemporary constitutional conundrum can be partially attributed to the problem of senate reform. Mr. Getty wants a triple E senate, M. Bourassa doesn't and others prefer that it be abolished. I hereby wish to propose a quadruple E senate which, I claim, would be agreeable to everyone.

The New Math, which was introduced into our schools in the 60's, is based on the elements of Set Theory. Thus, as everyone knows, anything you care to say about a member of the empty set (l'ensemble vide) is true because the empty set has no members.

I therefore propose that the senate be EMPTY. This is equivalent to abolishing it but has the advantage of being quadruple E and thus satisfying everyone. In an empty senate each province would have an EQUAL number of senators (zero). The provinces would have proportional representation; if Quebec has m consumers and Alberta has n then m . 0 = n . 0 = 0. Every member of the empty senate would be ELECTED. Moreover, an empty senate would clearly be at least as EFFECTIVE as our present senate.

An empty senate would have many other desirable features. For example, each of its members would be bilingual and, no matter what the salary scale, it would cost us nothing.

Notes of the Can. Math. Soc., April 1992

An Ode To Fréchet

Some time ago, in Riemann's day,
Calculus was penned in a cumbersome way;
seas of partials, indicies too,
Jacobian determinants spiced the stew.
But now we have another way;
linear maps have joined the fray.
'Though some feel wrath, me thinks that Math
hath truly felt a "breath of Fréchet."

The Amer. Math. Monthly, Nov. 1994

LaMent

A Mentor Emeritus of Kent
rendered havoc wherever she went.
For despite good intent,
she was seen to foment
in the mentored, demented torment

But the rabble of witless dissenters,
her boss viewed as petty fomenters.
So promoted she was
to the loftier cause
of mentoring apprenticing mentors

Watbard

From when mentoring was really in, eh?

Affiliation: 
University of Waterloo

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