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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.
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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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`
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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.
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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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