John Locker

B.S.E.:   University of Michigan

M.S.:     University of Michigan

Ph. D.:   University of Michigan

Specializations:  Spectral Theory, Two-Point Differential Operators

Office:  Retired, May, 2004

Phone:  970-482-4875 (home)

Email:  locker@math.colostate.edu  

Professor Locker began his career in teaching and research at the University of Minnesota in 1965, where he was a Dunham Jackson Research Instructor.  In 1967 he joined the Mathematics Department of Colorado State University as an Assistant Professor, rising to the rank of Professor in 1975.  During his many years at Colorado State he has taught mathematics courses ranging from calculus at the freshman level to functional analysis and spectral theory at the advanced graduate level.  In 1980 he was awarded the Oliver P. Pennock Distinguished Service Award for excellence in teaching.  Throughout his career Professor Locker has been an active research mathematician, publishing papers in the areas of nonlinear boundary value problems, numerical solution of differential and integral equations, regularization methods, and most recently, the spectral theory of two-point differential operators.

Selected Publications:

1.  Patrick Lang and John Locker, Spectral Decomposition of a Hilbert Space by a Fredholm Operator, J. Funct. Anal. 79 (1988),  9-17

2. Patrick Lang and John Locker, Spectral Representation of the Resolvent of a Discrete Operator, J. Funct. Anal. 79 (1988),  18-31

3. Patrick Lang and John Locker, Denseness of the Generalized Eigenvectors of an H-S Discrete Operator, J. Funct. Anal. 82 (1989),  316-329

4. Patrick Lang and John Locker, Spectral Theory for a Differential Operator: Characteristic Determinant and Green's Function, J. Math. Anal. Appl. 141 (1989),  405-423

5. Patrick Lang and John Locker, Spectral Theory of Two-Point Differential Operators Determined by -D².  I.  Spectral Properties, J. Math. Anal. Appl. 141 (1989),  538-558

6. Patrick Lang and John Locker, Spectral Theory of Two-Point Differential Operators Determined by -D².  II.  Analysis of Cases, J. Math. Anal. Appl. 146 (1990),  148-191

7. John Locker, The Nonspectral Birkhoff-Regular Differential Operators Determined by -D², J. Math. Anal. Appl. 154 (1991),  243-254

8. John Locker and Partick Lang, Eigenfunction Expansions for the Nonspectral Differential Operators Determined by -D², J. Differential Equations 96 (1992),  318-339

9.  John Locker, The Spectral Theory of Second Order Two-Point Differential Operators.  I.  Apriori Estimates for the Eigenvalues and Completeness, Proc. Roy. Soc. Edinburgh 121A (1992),  279-301

10.   John Locker, The Spectral Theory of Second Order Two-Point Differential Operators.  II.  Asymptotic Expansions and the Characteristic Determinant, J. Differential Equations 114 (1994), 272-287

11.   John Locker, The Spectral Theory of Second Order Two-Point Differential Operators.  III.  The Eigenvalues and Their Asymptotic Formulas, Rocky Mountain J. Math. 26 (1996), 679-706

12.   John Locker, The Spectral Theory of Second Order Two-Point Differential Operators.  IV.  The Associated Projections and the Subspace S^∞(L), Rocky Mountain J. Math. 26 (1996), 1473-1498

13.   John Locker, Functional Analysis and Two-Point Differential Operators, Pitman Research Notes in Mathematics, vol. 144, Longman, Harlow, Essex, 1986

14.  John Locker, Spectral Theory of Non-Self-Adjoint Differential Operators, Mathematical Surveys and Monographs, vol. 73, American Mathematical Society, Providence, R. I., 2000 

15.  John Locker, Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators, to appear in Memoirs of the American Mathematical Society     An unabridged version is available for downloading:

Eigenvalues and Completeness PDF

Eigenvalues and Completeness PS