@article {MR1452806, AUTHOR = {Hunt, Brian R.}, TITLE = {The {H}ausdorff dimension of graphs of {W}eierstrass functions}, JOURNAL = {Proc. Amer. f this is the caseth. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {126}, YEAR = {1998}, NUMBER = {3}, PAGES = {791--800}, ISSN = {0002-9939,1088-6826}, MRCLASS = {28A78 (42A32)}, MRNUMBER = {1452806}, MRREVIEWER = {Lars\ Olsen}, DOI = {10.1090/S0002-9939-98-04387-1}, URL = {https://doi.org/10.1090/S0002-9939-98-04387-1}, } @article {MR3391364, AUTHOR = {Cavalletti, Fabio}, TITLE = {A note on a residual subset of {L}ipschitz functions on metric spaces}, JOURNAL = {Proc. Edinb. Math. Soc. (2)}, FJOURNAL = {Proceedings of the Edinburgh Mathematical Society. Series II}, VOLUME = {58}, YEAR = {2015}, NUMBER = {3}, PAGES = {631--636}, ISSN = {0013-0915,1464-3839}, MRCLASS = {53C23 (30L10)}, MRNUMBER = {3391364}, MRREVIEWER = {Jes\'{u}s\ A.\ Jaramillo}, DOI = {10.1017/S0013091514000261}, URL = {https://doi.org/10.1017/S0013091514000261}, } @article {MR0555048, AUTHOR = {Mauldin, R. Daniel}, TITLE = {The set of continuous nowhere differentiable functions}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {83}, YEAR = {1979}, NUMBER = {1}, PAGES = {199--205}, ISSN = {0030-8730,1945-5844}, MRCLASS = {46E15 (26A27)}, MRNUMBER = {555048}, MRREVIEWER = {K.\ M.\ Garg}, URL = {http://projecteuclid.org/euclid.pjm/1102784670}, } @article{Saks1932, author = {Saks, S.}, journal = {Fundamenta Mathematicae}, keywords = {set theory, real functions}, language = {eng}, number = {1}, pages = {211-219}, title = {On the functions of Besicovitch in the space of continuous functions}, note = {http://eudml.org/doc/212573}, volume = {19}, year = {1932}, } @article{Banach1931, author = {Banach, S.}, journal = {Studia Mathematica}, language = {ger}, number = {1}, pages = {174-179}, title = {\"{U}ber die Baire'sche Kategorie gewisser Funktionenmengen}, note = {http://eudml.org/doc/217560}, volume = {3}, year = {1931}, } @article{Mazurkiewicz1931, author = {Mazurkiewicz, S.}, journal = {Studia Mathematica}, keywords = {set theory, real functions}, language = {fre}, number = {1}, pages = {92-94}, title = {Sur les fonctions non d\'{e}rivables}, note = {http://eudml.org/doc/217572}, volume = {3}, year = {1931}, } @article{Jarnik1933, author = {Jarn\'{i}k, V.}, journal = {Fundamenta Mathematicae}, keywords = {set theory, real functions}, language = {ger}, number = {1}, pages = {48-58}, title = {\"{U}ber die Differenzierbarkeit stetiger Funktionen}, note = {http://eudml.org/doc/212678}, volume = {21}, year = {1933}, } @article {MR1160715, AUTHOR = {Sagan, Hans}, TITLE = {An elementary proof that {S}choenberg's space-filling curve is nowhere differentiable}, JOURNAL = {Math. Mag.}, FJOURNAL = {Mathematics Magazine}, VOLUME = {65}, YEAR = {1992}, NUMBER = {2}, PAGES = {125--128}, ISSN = {0025-570X,1930-0980}, MRCLASS = {26A27}, MRNUMBER = {1160715}, DOI = {10.2307/2690494}, URL = {https://doi.org/10.2307/2690494}, } @article {MR1124993, AUTHOR = {Sagan, Hans}, TITLE = {Some reflections on the emergence of space-filling curves: the way it could have happened and should have happened, but did not happen}, JOURNAL = {J. Franklin Inst.}, FJOURNAL = {Journal of the Franklin Institute}, VOLUME = {328}, YEAR = {1991}, NUMBER = {4}, PAGES = {419--430}, ISSN = {0016-0032}, MRCLASS = {01A55 (01A60 26E99 54H99)}, MRNUMBER = {1124993}, MRREVIEWER = {Ryszard\ J.\ Pa\.{w}lak}, DOI = {10.1016/0016-0032(91)90017-W}, URL = {https://doi.org/10.1016/0016-0032(91)90017-W}, } @book {MR1299533, AUTHOR = {Sagan, Hans}, TITLE = {Space-filling curves}, SERIES = {Universitext}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {1994}, PAGES = {xvi+193}, ISBN = {0-387-94265-3}, MRCLASS = {00A05 (01A55 01A60 26-02)}, MRNUMBER = {1299533}, MRREVIEWER = {Ryszard\ J.\ Pa\.{w}lak}, DOI = {10.1007/978-1-4612-0871-6}, URL = {https://doi.org/10.1007/978-1-4612-0871-6}, } @article {MR1328375, AUTHOR = {Rodr\'{\i}guez-Piazza, L.}, TITLE = {Every separable {B}anach space is isometric to a space of continuous nowhere differentiable functions}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {123}, YEAR = {1995}, NUMBER = {12}, PAGES = {3649--3654}, ISSN = {0002-9939,1088-6826}, MRCLASS = {46B04 (26A27 46E15)}, MRNUMBER = {1328375}, MRREVIEWER = {Grzegorz\ Lewicki}, DOI = {10.2307/2161889}, URL = {https://doi.org/10.2307/2161889}, } @article {MR1707147, AUTHOR = {Hencl, Stanislav}, TITLE = {Isometrical embeddings of separable {B}anach spaces into the set of nowhere approximatively differentiable and nowhere {H}\"{o}lder functions}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {128}, YEAR = {2000}, NUMBER = {12}, PAGES = {3505--3511}, ISSN = {0002-9939,1088-6826}, MRCLASS = {46B20 (26A27 46E15)}, MRNUMBER = {1707147}, MRREVIEWER = {Grzegorz\ Lewicki}, DOI = {10.1090/S0002-9939-00-05595-7}, URL = {https://doi.org/10.1090/S0002-9939-00-05595-7}, } @article {MR0202936, AUTHOR = {Kiesswetter, Karl}, TITLE = {Ein einfaches {B}eispiel f\"{u}r eine {F}unktion, welche \"{u}berall stetig und nicht differenzierbar ist}, JOURNAL = {Math.-Phys. Semesterber.}, FJOURNAL = {Mathematisch-Physikalische Semesterberichte zur Pflege des Zusammenhangs von Schule und Universit\"{a}t}, VOLUME = {13}, YEAR = {1966}, PAGES = {216--221}, ISSN = {0340-4897}, MRCLASS = {26.41}, MRNUMBER = {202936}, } @book {MR2049443, TITLE = {Classics on fractals}, SERIES = {Studies in Nonlinearity}, EDITOR = {Edgar, Gerald A.}, PUBLISHER = {Westview Press. Advanced Book Program, Boulder, CO}, YEAR = {2004}, PAGES = {xii+366}, ISBN = {0-8133-4153-1}, MRCLASS = {28-06 (01A75 28-03 28A78 28A80)}, MRNUMBER = {2049443}, MRREVIEWER = {Yimin\ Xiao}, } @mastersthesis{johan2003, title={Continuous {N}owhere {D}ifferentiable {F}unctions}, author={Thim, Johan}, year={2003}, school={Lule\aa {} {U}niversity of {T}echnology }, note={ https://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-49636}, } @article{cellerier1890note, title={Note sur les principes fondamentaux de l'analyse}, author={Cell{\'e}rier, Charles}, pages={142--160}, journal={Darboux Bull.}, volume={14}, year={1890} } @book {MR1411907, AUTHOR = {Boas, Ralph P.}, TITLE = {A primer of real functions}, SERIES = {Carus Mathematical Monographs}, VOLUME = {13}, EDITION = {Fourth}, NOTE = {Revised and with a preface by Harold P. Boas}, PUBLISHER = {Mathematical Association of America, Washington, DC}, YEAR = {1996}, PAGES = {xiv+305}, ISBN = {0-88385-029-X}, MRCLASS = {26-01}, MRNUMBER = {1411907}, } @article {MR0864753, AUTHOR = {Luther, Wolfram}, TITLE = {The differentiability of {F}ourier gap series and ``{R}iemann's example'' of a continuous, nondifferentiable function}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {48}, YEAR = {1986}, NUMBER = {3}, PAGES = {303--321}, ISSN = {0021-9045,1096-0430}, MRCLASS = {42A55 (40E05)}, MRNUMBER = {864753}, MRREVIEWER = {H.\ Burkill}, DOI = {10.1016/0021-9045(86)90053-5}, URL = {https://doi.org/10.1016/0021-9045(86)90053-5}, } @article {MR2587578, AUTHOR = {Johnsen, Jon}, TITLE = {Simple proofs of nowhere-differentiability for {W}eierstrass's function and cases of slow growth}, JOURNAL = {J. Fourier Anal. Appl.}, FJOURNAL = {The Journal of Fourier Analysis and Applications}, VOLUME = {16}, YEAR = {2010}, NUMBER = {1}, PAGES = {17--33}, ISSN = {1069-5869,1531-5851}, MRCLASS = {26A27 (42A55)}, MRNUMBER = {2587578}, MRREVIEWER = {Jasson\ Vindas}, DOI = {10.1007/s00041-009-9072-2}, URL = {https://doi.org/10.1007/s00041-009-9072-2}, } @article {MR1461263, AUTHOR = {Sun, Daochun and Wen, Zhiying}, TITLE = {The {H}ausdorff dimension of graph of a class of {W}eierstrass functions}, JOURNAL = {Progr. Natur. Sci. (English Ed.)}, FJOURNAL = {Progress in Natural Science. English Edition}, VOLUME = {6}, YEAR = {1996}, NUMBER = {5}, PAGES = {547--553}, ISSN = {1002-0071,1745-5391}, MRCLASS = {28A78 (26A27)}, MRNUMBER = {1461263}, } @incollection {MR3558151, AUTHOR = {Bara\'{n}ski, Krzysztof}, TITLE = {Dimension of the graphs of the {W}eierstrass-type functions}, BOOKTITLE = {Fractal geometry and stochastics {V}}, SERIES = {Progr. Probab.}, VOLUME = {70}, PAGES = {77--91}, PUBLISHER = {Birkh\"{a}user/Springer, Cham}, YEAR = {2015}, ISBN = {978-3-319-18660-3; 978-3-319-18659-7}, MRCLASS = {28A78 (28A80)}, MRNUMBER = {3558151}, DOI = {10.1007/978-3-319-18660-3\_5}, URL = {https://doi.org/10.1007/978-3-319-18660-3_5}, } @article {MR3606737, AUTHOR = {Keller, Gerhard}, TITLE = {A simpler proof for the dimension of the graph of the classical {W}eierstrass function}, JOURNAL = {Ann. Inst. Henri Poincar\'{e} Probab. Stat.}, FJOURNAL = {Annales de l'Institut Henri Poincar\'{e} Probabilit\'{e}s et Statistiques}, VOLUME = {53}, YEAR = {2017}, NUMBER = {1}, PAGES = {169--181}, ISSN = {0246-0203,1778-7017}, MRCLASS = {37D20 (37D45 37G35 37H20)}, MRNUMBER = {3606737}, MRREVIEWER = {Leonardo\ E.\ Mora}, DOI = {10.1214/15-AIHP711}, URL = {https://doi.org/10.1214/15-AIHP711}, } @article {MR0640257, AUTHOR = {Itatsu, Seiichi}, TITLE = {Differentiability of {R}iemann's function}, JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.}, FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences}, VOLUME = {57}, YEAR = {1981}, NUMBER = {10}, PAGES = {492--495}, ISSN = {0386-2194}, MRCLASS = {42A16 (10H99 33A25)}, MRNUMBER = {640257}, MRREVIEWER = {S.\ L.\ Segal}, URL = {http://projecteuclid.org/euclid.pja/1195516225}, } @article {MR0715889, AUTHOR = {Smith, Arthur}, TITLE = {Correction to: ``{T}he differentiability of {R}iemann's function'' [{P}roc. {A}mer. {M}ath. {S}oc. {\bf 34} (1972), 463--468; {MR}0308337 (46 \#7451)]}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {89}, YEAR = {1983}, NUMBER = {3}, PAGES = {567--568}, ISSN = {0002-9939,1088-6826}, MRCLASS = {26A27}, MRNUMBER = {715889}, MRREVIEWER = {K.\ M.\ Garg}, DOI = {10.2307/2045519}, URL = {https://doi.org/10.2307/2045519}, } @article {MR0308337, AUTHOR = {Smith, A.}, TITLE = {The differentiability of {R}iemann's functions}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {34}, YEAR = {1972}, PAGES = {463--468}, ISSN = {0002-9939,1088-6826}, MRCLASS = {26A27}, MRNUMBER = {308337}, MRREVIEWER = {K.\ M.\ Garg}, DOI = {10.2307/2038391}, URL = {https://doi.org/10.2307/2038391}, } @article {MR1501044, AUTHOR = {Hardy, G. H.}, TITLE = {Weierstrass's non-differentiable function}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {17}, YEAR = {1916}, NUMBER = {3}, PAGES = {301--325}, ISSN = {0002-9947,1088-6850}, MRCLASS = {26A27}, MRNUMBER = {1501044}, DOI = {10.2307/1989005}, URL = {https://doi.org/10.2307/1989005}, } @book {MR3155290, AUTHOR = {Titchmarsh, E. C.}, TITLE = {The theory of functions}, NOTE = {Reprint of the second (1939) edition}, PUBLISHER = {Oxford University Press, Oxford}, YEAR = {1958}, PAGES = {x+454}, MRCLASS = {30-01 (26-01 28-01)}, MRNUMBER = {3155290}, } @article {MR3882060, AUTHOR = {Hocutt, J. A. and Robinson, P. L.}, TITLE = {Everywhere differentiable, nowhere continuous functions}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {American Mathematical Monthly}, VOLUME = {125}, YEAR = {2018}, NUMBER = {10}, PAGES = {923--928}, ISSN = {0002-9890,1930-0972}, MRCLASS = {26A24 (26A15)}, MRNUMBER = {3882060}, MRREVIEWER = {Rotraut\ Goubau\ Cahill}, DOI = {10.1080/00029890.2018.1517569}, URL = {https://doi.org/10.1080/00029890.2018.1517569}, } @book {MR3444902, AUTHOR = {Jarnicki, Marek and Pflug, Peter}, TITLE = {Continuous nowhere differentiable functions}, SERIES = {Springer Monographs in Mathematics}, NOTE = {The monsters of analysis}, PUBLISHER = {Springer, Cham}, YEAR = {2015}, PAGES = {xii+299}, ISBN = {978-3-319-12669-2; 978-3-319-12670-8}, MRCLASS = {26-01 (26A15 26A27)}, MRNUMBER = {3444902}, MRREVIEWER = {Robert\ W.\ Vallin}, DOI = {10.1007/978-3-319-12670-8}, URL = {https://doi.org/10.1007/978-3-319-12670-8}, } @article {MR1680194, AUTHOR = {Chamizo, Fernando and C\'{o}rdoba, Antonio}, TITLE = {Differentiability and dimension of some fractal {F}ourier series}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {142}, YEAR = {1999}, NUMBER = {2}, PAGES = {335--354}, ISSN = {0001-8708,1090-2082}, MRCLASS = {42A16 (11K41 26A24 28A78 28A80)}, MRNUMBER = {1680194}, MRREVIEWER = {Steen\ Pedersen}, DOI = {10.1006/aima.1998.1792}, URL = {https://doi.org/10.1006/aima.1998.1792}, } @article {MR0276422, AUTHOR = {Gerver, Joseph}, TITLE = {More on the differentiability of the {R}iemann function}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {93}, YEAR = {1971}, PAGES = {33--41}, ISSN = {0002-9327,1080-6377}, MRCLASS = {26.41}, MRNUMBER = {276422}, MRREVIEWER = {A.\ M.\ Bruckner}, DOI = {10.2307/2373445}, URL = {https://doi.org/10.2307/2373445}, } @article {Takagi1901, AUTHOR = {Takagi, Teiji}, TITLE = {A simple example of the continuous function without derivative (誘導函數ヲ有セザル連續函數ノ簡單ナル例)}, JOURNAL = {Tokyo Sugaku-Butsurigakkwai Hokoku}, VOLUME = {1}, YEAR = {1901}, PAGES = {F176--F177}, DOI = {10.11429/subutsuhokoku1901.1.F176}, }