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Anthony G. O'Farrell: Publications




Books:
1. A. O Fearghail. Notai an Bhrathar Mac Craith. Institiud Oideachais Marino. 2002. iv+170pp. ISBN 1-8991-6223-2
2. G. McGuire, A.G. O'Farrell, D. Redmond, R.O. Watson and D. Wraith. Maynooth Mathematical Olympiad Manual. Kilcock. Logic Press. 2002. viii+143pp. ISBN 0-9544269-0-8.
3. A.G. O'Farrell. Introduction to Maple Programming. Kilcock. Logic Press. 2005. viii+235pp. ISBN 0-9544269-4-0.
4. J. Cruickshank, G. McGuire, A.G. O'Farrell, D. Redmond, R.O. Watson and D. Wraith. Irish Mathematical Olympiad Manual. Kilcock. Logic Press. 2008. viii+165pp. ISBN 0-9544269-7-5.
5. A.G. O'Farrell and I. Short. Reversibility in Dynamics and Group Theory. LMS Lecture Notes Series: 416. Cambridge University Press. 2015. xi+281pp. ISBN 978-1-107-44288-7.
6. J. Cruickshank, G. McGuire, A.G. O'Farrell, D. Redmond, R.O. Watson and D. Wraith. Irish Mathematical Olympiad Manual. Kilcock. Logic Press. Second Edition. 2013. viii+166pp. ISBN 978-0-9544269-8-9.
7. A.G. O'Farrell. Analysis Zero. Kilcock. Logic Press. 2015. ISBN 978-1-326-41433-7 (hardcover), 978-1-326-41581-5 (paperback).
8. A.G. O'Farrell. Analysis One. Kilcock. Logic Press. 2017. ISBN 978-0-244-02530-4 (hardcover). Free ebook available.

Research Papers in Mathematics:
Recent papers may be found on ArXiv using my public author identifier, http://arxiv.org/a/ofarrell_a_1.
1. Thesis: Capacities in Uniform Approximation, Brown University, 1973.
2. An isolated bounded point derivation, Proceedings AMS 39 (1973) 559-562.
3. Removable sets for classes of functions, Proceedings AMS 41 (1973) 282-286.
4. Equiconvergence of derivations, Pacific J. Math. 53 (1974) 539-554.
5. Density of parts of algebras on the plane , Transactions AMS 196 (1974) 403-414.
6. Analytic capacity, Holder conditions, and $\tau$-spikes, Transactions AMS 196 (1974) 415-424.
7. A generalized Walsh-Lebesgue theorem, Proc. Roy. Soc. Edinburgh 73A(1974/75) 231-234.
8. Lipschitz functions and bad metrics, Michigan Math. J. 21 (1974) 277-287.
9. Lip 1 rational approximation, Journal LMS (2) 11 (1975) 159-164.
10. Hausdorff content and rational approximation in fractional Lipschitz norms, Transactions AMS 228 (1977) 187-206.
11. Annihilators of rational modules, J. Functional Analysis 19 (1975) 373-389.
12. Localness of certain Banach modules, Indiana Univ. Math. J. 24 (1975) 1135-1141.
13. Metaharmonic approximation in Lipschitz norms, Proc. Roy. Irish Acad. 75A (1975) 317-330.
14. Continuity properties of Hausdorff content, Journal LMS (2) 13 (1976) 403-410.
15. (with J.B. Garnett) Sobolev approximation by a sum of subalgebras on the circle, Pacific J. Math. 65 (1976) 55-63.
16. (with D.E. Marshall) Uniform approximation by real functions, Fund. Math., 54 (1979) 203-211.
17. Functions with smooth extensions, Proceedings RIA 74A (1974) 317-320.
18. Rational approximation in Lipschitz norms I, Proceedings RIA 77A (1977) 113-115.
19. Rational approximation in Lipschitz norms II, Proceedings RIA 79A (1979) 103-114.
20. A Characterisation of harmonic functions, Proceedings RIA 78A (1978) 33-36.
21. Point derivations on an algebra of Lipschitz functions, Proceedings RIA 80A (1980) 23-39.
22. Analytic capacity and equicontinuity, Bulletin LMS, 10 (1978) 276-279.
23. A regular uniform algebrea with a continuous point derivation of infinite order, Bulletin LMS, 11 (1979) 41-44.
24. Estimates for capacities and approximation in Lipschitz norms, J.f.d. Reine u. Angew. Math. 311/312 (1979) 101-115.
25. Real parts of analytic functions, Proceedings RIA 79A (1979) 173-178.
26. (with K.J. Preskenis) Approximation by polynomials in two complex variables, Math. Ann. 246 (1980) 225-232.
27. Restriction algebras, Proceedings RIA 82A (1982) 105-108. MR 84b:46058 (The reviewer is wrong: cf. MR Annual Index 1984, Errata and Addenda, page (i).)
28. (with D. Marshall) Approximation by a sum of two algebras. The lightning bolt principle. Journal of Functional Analysis, 52 (1983) 353-368.
29. The Legendre expansion of a smooth function, in Mathematical Structures-Computational Mathematics-Mathematical Modelling, Sofia 1984, pp.165-169.
30. (with K.J. Preskenis and D. Walsh) Polynomial approximation on graphs, Math. Ann. 226 (1983) 73-81.
31. Polynomial approximation of smooth functions, Journal LMS, (2) 28 (1983) 496-506.
32. (with K.J. Preskenis and D. Walsh) Holomorphic approximation in Lipschitz norms, Contemporary Mathematics 32 (1984) 187-194.
33. (with K.J. Preskenis) Approximation by polynomials in two diffeomorphisms, Bulletin AMS, 10 (1984) 105-107.
34. Instability pairs, Proceedings RIA 86A (1986) 67-80. MR88a:28006
35. Rational approximation and weak analyticity I, Math. Ann. 273 (1986) 375-381. MR87d:30041
36. Rational approximation and weak analyticity II, Math. Ann. 281 (1988) 169-176. MR 89k: 30036
37. A simplified proof of Vitushkin's squares theorem, Proceedings RIA 87A (1987) 91-94. MR 89e: 30067.
38. (with G.R. Allen and T.J. Ransford) A Tauberian theorem arising in operator theory, Bulletin L.M.S. 19 (1987) 537-545. MR 89c: 47003
39. $C^\infty$ maps may increase $C^\infty$ dimension, Inventiones Math. 89 (1987) 663-668. MR 89d: 58022. A preprint appeared as IHES preprint M/86/47 (1986).
40. The order of a symmetric concrete space, Proceedings RIA 88A (1988) 39-48. MR 90b: 46081.
41. (with K.J. Preskenis) Uniform approximation by polynomials in two functions, Math. Ann. 284 (1989) 529-35. Announced in AMS Abstracts 9 (1988) 86 (no. 839-46-90). MR 90k: 30077.
42. The 1-reduction for removable singularities, and the negative H\"older spaces, Proceedings RIA. 88A (1988) 133-151. MR 90g: 35003.
43. (with D. O'Regan) Existence results for some initial and boundary value problems, Proceedings AMS, 110 (1990) 661-73.
44. (with R.O. Watson) The tangent stars of a set, and extensions of smooth functions, J. f\"ur die Reine und Angew. Math., 430 (1992) 109-137. Announced in: Bulletin IMS 26 (1991) 10-1. MR 93h:58015.
45. (with F. Perez-Gonzalez) Pointwise bounded approximation by polynomials, Math. Proc. Camb. Phil. Soc. 112 (1992) 147-155. MR 93d:30048.
46. (with D. Lord) Removable singularities for analytic functions of Zygmund class, Proceedings R.I.A., 91A (1991) 195-204. MR 93h:30036.
47. T-invariance, Proceedings R.I.A. 92A (1992) 185-203.
48. (with P. de Paepe) Approximation on a disk II, Math. Zeit. 212 (1993) 153-6.
49. (with D.J. Lord) Boundary smoothness properties of Lip$\alpha$ analytic functions , J. Analyse Math. (Jerusalem), 63 (1994) 103-19.
50. (with S. Dineen, J. Feinstein, and R.M. Timoney) A fixed point theorem for holomorphic maps, Proceedings R.I.A., 94A (1994) 77-84.
51. (with R.O. Watson) Constructing C$^1$ extensions, Proceedings RIA 93A (1993) 61-72.
52. (with J. Feinstein and H. Lande) Approximation and extension in normed spaces of infinitely-differentiable functions, J.L.M.S. (2) 54 (1996) 541-56.
53. (with T. Dowling) Affine transformations and analytic capacities, Transactions A.M.S., 347 (1995) 2643-55.
54. (with F. O'Cairbre and A. O'Reilly) Bistability, bifurcation and chaos in a laser system, Int. J. Bifurcation and Chaos, 5 (1995) 1021-31.
55. (with T. Dowling) Sobolev space analytic capacities , Proceedings R.I.A., 97A (1997) 87-99.
56. An example on Sobolev space approximation, Bulletin L.M.S., 29 (1997) 470-4.
57. (with G. Allan, G. Kakiko and R. Watson) Finitely-generated algebras of smooth functions in one dimension , J. Functional Analysis, 158 (1998) 458-74.
58. (with G. Allan, G. Kakiko and R. Watson) Algebras of smooth functions , in E. Albrecht and M. Mathieu (eds), Banach Algebras '97. W. de Gruyter. Berlin. 1998. pp. 43-53.
59. (with G. Allan, G. Kakiko and R. Watson) Localness of A(\Psi) algebras , Math. Proc. Roy. Ir. Acad., 101A (1) (2001) 61-70.
60. (with I. Netuka and A. Sanabria) Pervasive algebras of analytic functions. J. Approx. Theory, 106 (2000) 262--75.
61. (with A. Sanabria) Pervasive algebras of analytic functions on Riemann surfaces. Math. Proc. Roy. Ir. Acad., 101A (1) (2001) 87-94.
62. (with D. Graham and S. Keane) Sim\'eadracht amch\'ulaithe ch\'orais dinimici\'uil, (Time--reversal symmetries of dynamical systems) Proc. Irish Systems and Signals Conference, Maynooth, 2001, pp. 27-31. (An English--language version is available.)
63. (with A. Sanabria) De Paepe's disc has nontrivial polynomial hull , Bull. LMS, 34 (2002) 490-4.
64. Compositions of involutive power series and reversible series. Comput. Methods Funct. Theory 8 (2008) 173-93.
65. When uniformly-continuous implies bounded. Bulletin Ir. Math. Soc. 53 (2004) 53-6.
66. Conjugacy, involutions, and reversibility for real homeomorphisms, Bulletin Ir. Math. Soc. 54 (2004) 41-52. Corrigendum: 55 (2005) 61. Corrigendum secundum: 56 (2005) 15.
67. (with M. Roginskaya) Conjugacy of real diffeomorphisms. A Survey. , Algebra i Analiz, 22 (2010) 3-56. arXiv:0911.0804 =St. Petersburg Math. J. (1) 22 (2011) 1-40.
68. (with R. Lavicka and Ian Short) Reversible maps in the group of quaternionic M\"obius transformations . Math. Proc. Camb. Phil. Soc., 143 (2007) 57-69.
69. (with Ian Short) Reversibility in the diffeomorphism group of the real line. Publicacions Matematiques, 53 (2009) 401-15. arXiv:0811.3597
70. (with Nick Gill and Ian Short) Reversibility in the group of homeomorphisms of the circle. Bulletin LMS 41 (2009) 885-97; doi: 10.1112/blms/bdp065 permanent free online access at blms.oxfordjournals.org and arXiv:0710.3997
71. (with M. Roginskaya) Reducing conjugacy in the full diffeomorphism group of R to conjugacy in the subgroup of orientation-preserving maps. Zapiski Nauchnykh Seminar POMI RAN (Russian) 360 (2008) 231-7. = J. Math. Sci. 158 (2009) 895-8. arXiv:0811.3370
72. (with P. Ahern) Reversible biholomorphic germs. Comput. Methods Funct. Theory 9 (2009), No. 2, 473--84. arXiv:0811.1575
73. (with Jesus San Martin) A general stability criterion for switched linear systems having stable and unstable subsystems. Int. J. Adaptive Control Signal Processing 27 (2013) 1000-11. doi: 10.1002/acs.2373 arXiv:0811.1575 Wiley online version 6 Dec (2012)
74. (with Frederic Le Roux, Maria Roginskaya and Ian Short) Flowability of plane homeomorphisms. Ann. Inst. Fourier, 62 (2012) 619-39. ArXiv:0912.2012
75. (with Stephen M. Buckley) Wiring switches to light bulbs. Preprint. 2010. arXiv:1101.4922
76. (with Pamela Gorkin) Pervasive algebras and maximal subalgebras. Studia Math. 206 (2011) 1-24. ArXiv:1005.0719 Digital Commons at Bucknell. Online Version. doi:10.4064/sm206-1-1.
77. (with Dmitri Zaitsev) Formally-reversible maps of (C^2,0). Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 13 (2014) 371-97. doi:10.2422/2036-2145.201201_001 ArXiv:1111.6984
78. (with Dmitri Zaitsev) Factorising formal maps into reversible or involutive factors. J. Algebra 399 (2014) 657-74. doi: 10.1016/j.jalgebra.2013.09.053 http://arxiv.org/abs/1310.4857
79. (with Azadeh Nikou) Banach algebras of vector-valued functions. Glasgow Math J 56 (2014) 419-26. doi:10.1017/S0017089513000359. Corrigendum: Glasgow Math J (2019) doi:10.1017/S0017089519000351. http://arxiv.org/abs/1305.2751
80. (with Azadeh Nikou) Ditkin conditions. Glasgow Math J 60 (2017) 153-63. doi:10.1017/S0017089516000628 http://arxiv.org/abs/1512.09303
81. Boundary smoothness of analytic functions. Analysis and Mathematical Physics, 4 (2014) 131-44. doi: 10.1007/s13324-014-0074-0 http://arxiv.org/abs/1402.4307 http://link.springer.com/journal/13324/4/1/page/1
82. Derivatives at the Boundary for Analytic Lipschitz Functions. (Russian) Mat. Sbornik 207(2016)119-40. doi:10.4213/sm8629 http://arxiv.org/abs/1605.05196
83. Boundary values of holomorphic distributions in negative Lipschitz classes, in H. Garth Dales, Dmitry Khavinson, and Javad Mashreghi (eds), Complex Analysis and Spectral Theory. Contemporary Mathematics 743 (2020) 151-179. http://arxiv.org/abs/1806.09979
84. (with Gavin Armstrong) Dimension of Images of Large Level Sets. Math.Scand. 128 (2022) 147-160. doi:10.7146/math.scand.a-129246. http://arxiv.org/abs/2010.11556
85. Riordan group in d dimensions. 2020. http://arxiv.org/abs/2009.14130
86. Centralisers of formal maps. 2020. http://arxiv.org/abs/2010.07177



Expository Papers in Mathematics:
1. (with W.J. Kirk) Roots of real polynomials, IMS Newsletter 4 (1981) 24-27.
2. (with A. O'Cairbre) News for complex variables teachers, IMS Newsletter 5 (1982) 28-30.
3. Theorems of Walsh-Lebesgue type, in Aspects of Contemporary Complex Analysis, ed. Brannan and Clunie, Academic Press 1980, pp.461467.
4. Five generalisations of the Weierstrass approximation theorem, Proceedings RIA, 81A (1981) 65-69.
5. Complex powers, IMTA Newsletter 49 (1982) 18-32.
6. Qualitative rational approximation on plane compacta, in Lectures in Banach Spaces, Harmonic Analysis, and Probability, LNM995 Springer 1983, pp.103-122.
7. Restrictions of uniform algebras, in Complex Analysis and Applications 1981, Sofia 1984, pp.161-166. MR 88e:46042
8. Capacities, analytic and other, IMS Newsletter 13 (1985) 48-56. +Erratum, IMS Bulletin 16 (1986) 35, MR88a:30054ab
9. Rabbit Mathematics, IMTA Newsletter 58 (1985) 30-40.
10. A series of surprises , IMTA Newsletter 73 (1990) 28-33.
11. Capacities in function theory, in Potential Theory, ed. M. Kishi, Walther de Gruyter, Berlin, New York. 1991. pp. 93-105. MR 93j:30001.
12. Notes on the Symmetric Concrete Spaces. Maynooth Lecture Notes. 1990. (102+iii pp.)
13. Research in progress , March 2000. Maynooth University Record (2000) 89--92.
14. The Western Front. IMS Bulletin 57 (2006) 81-91.
15. A Quaternionic Gem. IMTA Newsletter 105 (2006) 16-25.
16. Greenberg's betweenness axioms. To appear.
17. A little help from my friends. IMS Bulletin 64 (2009) 31-42. ArXiv:1101.4623
18. Integral binomial coefficients. Irish Undergraduate Mathematical Magazine 2 (2013) 15-8.
19. Reversibility questions in groups arising in analysis. CRM Proceedings and Lecture Notes 55 (2012) 293-300. Arxiv:1110.6353 (The title was changed at referee's suggestion. Original title: Reversibility and Banach Algebras)
20. (with Patrick D. Barry) Geometry in the transition from primary to post-primary. IMTA Newsletter 114 (2014) 22-39. Arxiv:1407.5499a Final Printed Version

Book reviews:
1. David R. Adams and Lars Inge Hedberg. Function Spaces and Potential Theory. Bull. LMS (1996)
2. Reuben Hersh and Vera John-Steiner. Loving + Hating Mathematics. Bull. IMS 67 (2011) 95-9.
3. Dana Mackenzie. The Universe in Zero Words. Bull. IMS 69 (2012) 63-6.
4. Zvi Artstein. Mathematics and the Real World. LMS Newsletter No.446 April 2015, pp. 40-1.
5. Anthony Lo Bello. Origins of Mathematical Words. Bulletin IMS 80 (2017) 72-7.
6. Ronald S.Calinger: Leonhard Euler: Mathematical genius of the enlightenment. Bulletin IMS 87 (2021) 87-89.

Problems: 1. AMM problems solved: Problem E1822, 84(1977)569-570; Problem 6051, 84(1977) 492; Problem 6165 86(1979) 229-30. I also posed a few in the 1970's.
2. (With Maria Roginskaya) Inequality for number of sums. To appear.
3. (With Vassily Bernik) Some problems about area and perimeter. IMTA Newsletter 110 (2010) 14-22.
4. Lockscreen hack. 5. Uniform approximation by Harmonic Functions. Problem 12.15 in Linear and Complex Analysis, Problem Book 3, Part 2. LNM 1574 p.121. 1994. (Solved by Maxim Ya Mazaloff. Proc Steklov Math Inst. 279 (2012) 110-154.) `:w

Math. Reviews: 66 reviews, in the period 1975--93.

Zentralblatt f. Math. Reviews: Reviews in the period 2012-present.


Non-Mathematical Work:

1. The interpretation of Megalithic art.

Principles for the interpretation of megalithic art, to appear.

2. The causes of Multiple Sclerosis.
(with E. Keelan, D. Lord, and H. Staunton) Application of oligogenetic calculus to MS, presented at Irish Neurological Association, May 1988.
(with D.Lord, H.Staunton, and E.Keelan) MS susceptibility is determined by an autosomal locus and an X-locus, presented at the World Congress of Neurology, New Delhi, October 1989.
(with D.Lord, H.Staunton, and E.Keelan) The inheritance of MS susceptibility, Ir. J. Med. Sci. 159, Supplement 8 (1990) 1-20.
(with D.Lord, H.Staunton, and E.Keelan) The inheritance of MS susceptibility, IFMSS Update 4 (1991) 16.
The inheritance of MS susceptibility, IFMSS Annual Conference Abstracts 1990, p. 10.

3. Humour.
A Sociological Question, IMS Bulletin 19 (1987) 49-51.
Letter to the Editor. IMS Bulletin 53 (2004) 11.

4. Various.
1. Tribute to Brother Fabian McGrath. Drimnagh Castle CBS 50th Anniversary volume. 2004.
2. Tribute to Philip Gormley. In Jennifer Gormley. The Life and Times of Paddy Gormley. Sperrin. Goshaden, Co. Derry. 2004.
3. Tribute to William Curtis (Fr. Emmanuel) OCSO, in Liam Maher's History of the Cistercian College, Roscrea. 2004.
4. Welcome address to First Science Mathematics. In Thomas A.F. Kelly (ed), What Price the University?, NUI Maynooth. 2006. pp 182-8.
5. School Geometry. IMTA Newsletter 109 (2009) 21-8.
6. Appendix to the Schools Syllabus Documents: Geometry Course for Post-primary School Mathematics. NCCA. 2008. (2008 draft) 45pp. Download latest from NCCA website. It is currently (2018) Appendix B
7. Editorials in the Bulletin of the Irish Math Soc:
67 (Summer 2011) 68 (Winter 2011) 69 (Summer 2012)
70 (Winter 2012) 71 (Summer 2013) 72 (Winter 2013) 73 (Summer 2014) 74 (Winter 2014) 75 (Summer 2015) 76 (Winter 2015) 77 (Summer 2016) 78 (Winter 2016) 79 (Summer 2017)
80 (Winter 2017)
81 (Summer 2018) 82 (Winter 2018) 83 (Summer 2019) 84 (Winter 2019) 85 (Summer 2020) 86 (Winter 2020) 87 (Summer 2021)
8. An Chéad Ollamh Tuata (The First Lay Professor), In Salvador Ryan and John-Paul Sheridan (eds), We Remember Maynooth. Messenger Publications. 2020.
9. (with T. Carroll et al.) Patrick Denis Barry: 1924--2021.
Contact Problems Research Interests Publications List Curriculum Vitae Research Collaboration NUIM Maths Dept Logic Press Blog
Revised 2-4-2022.