The University of York

 

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              Maurice Dodson

Monographs:

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Metric Diophantine approximation on manifolds (with V.I. Bernik), Cambridge Tracts in Mathematics No.137, CUP, 1999.

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Number Theory and Dynamical Systems (editor with J A G Vickers), LMS Lecture Note Series 134, Cambridge University Press, 1989.

Papers:

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The Whittaker-Kotel'nikov-Shannon theorem, spectral translates and Plancherel's formula (with M G Beaty), to appear in J. Four. Anal. Appl., 2004 .

`

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Hausdorff dimension and Diophantine approximation (with S. Kristensen), to appear in Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, AMS Proc. Symp. Pure Math, 2003 .

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Exceptional sets in dynamical systems and Diophantine approximation, in Proc. of Rigidity in dynamics and geometry conference (eds. M. Burger and A. Iozzi), Newton Inst., Cambridge, Springer Verlag 2002, 77-98.

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Regular systems, ubiquity and Diophantine approximation (with V. V. Beresnevich, V. I. Bernik), in A Panorama of Number Theory (ed. G. Wustholtz), CUP 2002, 260-279.

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Shannon's sampling theorem, incongruent residue classes and Plancherel's theorem, Sem. th. nomb. Bord. 14 (2002), 425-437.

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Simultaneous Diophantine approximation on the circle and Hausdorff dimension (with H. Dickinson), Math. Proc. Camb. Phil. Soc., 130 (2001), 515-522.

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Extremal manifolds and Hausdorff dimension (with H.Dickinson), Duke Math. J., 101 (2000), 271-281.

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On linear manifolds satisfying Khintchine's approximation theorem (with V. V. Beresnevich and V. I. Bernik), (in Byelorussian), Proc. Acad. Sci. Belarus, Series: Math. Physics, No 2, 2000, 14-17.

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Abstract harmonic analysis and the sampling theorem (with M G Beaty), in "Fourier Analysis and Sampling Theory: Advanced Topics" (eds J.R.Higgins and R.Stens), Oxford University Press, 1999, 233-265.

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Hausdorff dimension and p-adic Diophantine approximation (with H.Dickinson and J.Yuan), Indag. Mathem., N.S.10 (1999), 337-347.

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The Khintchine-Groshev theorem for planar curves (with V.V.Beresnevich, V.I.Bernik, H.Dickinson), Proc. Roy. Soc. Lond. A, 455 (1999), 3053-3063.

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Extensions of Jarnik's work in Diophantine approximation, in "Life and work of Vojtech Jarnik" (B. Novak ed.), Society of Czech Mathematicians and Physicists, Prometheus, 1999, 23-35.

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Metric theory of Diophantine approximation in the field of complex numbers (with V.I.Bernik), in "Number Theory and its Applications" (S.Konemitsu and K.Gyory eds.), Kluwer Academic 1999, 51-58.

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An application of a general sampling theorem (with M.G.Beaty), Result. Math, 34 (1998), 241-254.

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A Khintchine-type extension of Schmidt's theorem for planar curves (with V.I. Bernik and H.Dickinson). Proc. Roy. Soc. Lond. A, 454 (1998), 179-185.

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A note on inhomogeneous metric Diophantine approximation, J. Australian Math. Soc. A, 62 (1997), 175-185.

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Inhomogeneous non-linear Diophantine approximation, (with V. V. Beresnevich and V. I. Bernik). In "Papers in honour of V.G.Sprindzuk's 60th birthday", 13-20, Institute of Mathematics, Belarus Academy of Sciences, Minsk (1997).

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Simultaneous Diophantine approximation and asymptotic formulae on manifolds (with B P Rynne and J A G Vickers), J. Number Theory 58 (1996), 298-316.

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The exact order of approximation of zero by values of integral complex polynomials, (with V.I.Bernik), Dokl. Akad. Navuk Belarus, 40 (1996), 10-14 (in Belarussian).

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Patterson measure and ubiquity (with M V Melian, D Pestana and S L Velani), Ann. Acad. Scien. Fenn. A, 40 (1995), 37-60.

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Approximating smoothed step functions by Paley-Wiener functions, (with M G Beaty and J R Higgins), J. Approx. Th. 78 (1994), 433-445.

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The Hausdorff dimension of exceptional sets associated with normal forms, (with B.P.Rynne and J.A.G.Vickers) J. London Math. Soc., 49 (1994), 614-624.

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Applications of multiband sampling theory to image processing, in "Communication Theory and Applications II" (eds. B Honary, M Darnell and P G Farrell), HW Communications Ltd, 1994, 345-353.

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The distribution of sampling rates for signals with equally spaced, equally wide spectral bands (with M G Beaty), SIAM J. Numer. Anal., 53 (1993), 893-906.

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Errors in reconstructing multiband signals (with M G Beaty), in "Communication Theory and Applications I" (eds. M Darnell, B Honary and P G Farrell), HW Communications, 1993, 96-102.

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Chord theorems, circle maps and the Borsuk-Ulam antipodal theorem, N. Z. J. Math., 22 (1993), 23-29.

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Geometrical and probabilistic ideas in metric Diophantine approximation, (in Russian) Usp. Mat. Nauk, 48 (1993), 77-106; also in Russian Math. Surveys 48 (1993), 72-103.

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Systems of linear forms and covers for star bodies (with S Hasan), Acta Arith. 61 (1992), 119-127

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Shannon's sampling theorem , Current Science 65 (1992), 253-260.

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Hausdorff dimension, lower order and Khintchine's theorem in Diophantine approximation, J. reine ange. Math., 432 (1992), 69-76.

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Hausdorff dimension of small divisors for lower dimensional KAM-tori (with J.Poeschel, B.P.Rynne and J.A.G.Vickers), Proc. Roy. Soc., A 439 (1992), 359-371.

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Khintchine-type theorems on manifolds (with B P Rynne and J A G Vickers), Acta Arith. 57 (1991), 115-130.

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Star bodies and Diophantine approximation , J. London Math. Soc., 44 (1991), 1-8.

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Diophantine approximation and a lower bound for Hausdorff dimension (with B P Rynne and J A G Vickers), Mathematika 37 (1990), 59-73.

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Diophantine inequalities and multiband sampling, in "Proc NATO ASI on Fourier Analysis and its Applications" (ed J S Byrnes and J L Byrnes) Il Ciocco, Italy, Kluwer Academic Publishers, Dordrecht, The Netherlands 1990, 483-498.

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Dirichlet's theorem and Diophantine approximation on manifolds (with B P Rynne and J A G Vickers), J. Number Theory 36 (1990), 85-88.

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Linear forms on manifolds (with B P Rynne and J A G Vickers), Proc. Indian Acad. Sci., 100 (1990), 221-229.

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Averaging in multi-frequency systems (with B.P.Rynne and J.A.G.Vickers), Nonlinearity 2 (1989), 137-148.

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Diophantine approximation, Hausdorff dimension and Schroeder's functional equation, Sem. Theorie Nombres de Bordeaux, Expose No 22, 1987-1988, 1-13.

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Adaptive-rate sampling applied to the storage and transmission of multiple band-pass signals (with M.Darnell, B.Honary and W.He), in "Proceedings of the Sixth International Conference of System Engineering" (ed N W Bellamy), Coventry Polytechnic, ICSE 1988, 109-119.

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Metric Diophantine approximation and Hausdorff dimension on manifolds (with B.P.Rynne and J.A.G.Vickers), Math. Proc. Camb. Philos. Soc., 105 (1989), 547-558.

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An algorithm for optimal regular sampling (with A M Silva), Signal Processing 17 (1989), 169-174.

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Derivative sampling for multiband signals (with M G Beaty), J. Numer Funct. Anal. Optim. 10 (1989), 875-898.

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The Hausdorff dimension of systems of linear forms (with J. D. Bovey), Acta Arith. 46 (1986), 337-358.

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Exceptional sets in Kolmogorov-Arnol'd-Moser Theory (with J.A.G.Vickers). J. Phys. A 19 (1986), 349-374.

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A note on Whittaker's cardinal series in harmonic analysis (with A M Silva and V Soucek) Proc. Edin. Math. Soc. (1986) 29, 349-357.

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Evoluzione e teoria della Catastrofe, Prometeus (1986) 1, 81-118.

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Fractal dimension of vegetation and the distribution of arthropod body lengths (with D R Morse, J H Lawton and M H Williamson), Nature 314 (1985), 731-733.

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Fourier analysis and the sampling theorem (with A M Silva), Proc. Roy. Irish Acad. 85A (1985), 81-108.

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A Brouwer type coincidence theorem and the fundamental theorem of algebra Can. Math. Bull. 27 (1984), 478-480.

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A note on the Hausdorff-Besicovitch dimension of systems of linear forms Acta Arith. 44 (1984), 87-98.

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Leray residues applied to solutions of the Laplace and wave equations (with V.Soucek). Sem. Geom., Univ. Stud. Bologna 1984, 93-107.

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Some estimates for diagonal equations over p-adic fields Acta Arith. 40 (1982), 118-124.

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Analysis of the extinction of the Late Cretaceous foraminifer Afrobolivina afra (with R A Reyment) Cretaceous Res. 1 (1980), 143-164.

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Thom's catastrophe theorem, In "Proceedings of the Ninth National Mathematics Conference" (ed J Zafarani), Isfahan, Iran, 1978, 70-88.

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Applications of Thom's catastrophe theorem to the phenotypic response of adaptive populations, In "Proceedings of the Ninth National Mathematics Conference" (ed J Zafarani), Isfahan, Iran, 1978, 89-104.

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The fractional dimension of sets whose rational approximations have errors with a small product (with J D Bovey). Bull. London Math. Soc. 10 (1978), 213-218.

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Simple nonlinear systems and the cusp catastrophe (with C T J Dodson) Bull. Inst. Math. Appls., 13 (1977), 77-85.

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Allopatric speciation and the fold catastrophe (with A Hallam), Amer. Naturalist 111 (1977), 415-433.

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Catastrophe Theory, Nature, 270 (1977), 658;

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A note on Waring's Problem in GF(p) (with A Tietavainen) Acta Arith. 30 (1976), 159-167.

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Darwin's Law of Natural Selection and Thom's Theory of Catastrophes, Math. Biosc. 28 (1976), 243-274.

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Quantum evolution and the fold catastrophe. Evol. Theory, 1 (1975), 107-118.

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Evolution and the Fold Catastrophe. In "Rencontre de Cargese sur les singularities et leurs applications" (ed F. Pham). Inst. d'Etudes Sc. Cargese, Cargese (1975), 126-127.

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Quantum evolution and the fold catastrophe. Evol. Theory, 1 (1975), 107-118.

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Evolution and the Fold Catastrophe. In "Rencontre de Cargese sur les singularities et leurs applications" (ed F. Pham). Inst. d'Etudes Sc. Cargese, Cargese (1975), 126-127.

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A note on additive equations over p-adic fields, Ann. Univ. Turku., Series A 164 (1974), 3-7.

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On a function due to S Chowla. J. Number Theory, 5 (1973), 287-292.

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Nilpotent topological groups. J. London Math. Soc. (2) 7 (1973), 239-245.

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On a function due to S Chowla. J. Number Theory, 5 (1973), 287-292.

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On Waring's Problem in p-adic fields. Acta Arith. 22 (1973), 315-327.

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On Waring's Problem in GF(p). Acta Arith. 19 (1971), 147-173.

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The average order of two arithmetic functions. Acta Arith. 16 (1969), 71-84.

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Homogeneous additive congruences. Phil. Trans. Roy. Soc., A 261 (1967), 163-210.

Preprints:

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The Shannon sampling theorem, abstract harmonic analysis and Haar measure (with M.G.Beaty).

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Commentary on `Der Paleysche Satz ueber Charaktere'. To appear in "The Collected Works of E.Landau", Volume 10, Thales, Essen.

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Metric inhomogeneous Diophantine approximation with integral polynomials (with V.I.Bernik and H.Dickinson)

     

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             Maurice Dodson
Last modified: 24 May 2004
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