Junior Research Team "Fractal Analysis"

Books

D.HAROSKE, TH.RUNST, H.-J. SCHMEISSER (ED.): Function Spaces, Differential Operators and Nonlinear Analysis. The Hans Triebel Anniversary Volume. Birkhäuser, Basel, 2003.
D.D. HAROSKE : Envelopes and sharp embeddings of function spaces.. Chapman & Hall/CRC Research Notes in Math., Boca Raton, Chapman & Hall/CRC, 2006.

Theses

1. E. TAMÁSI : Self-similar fractals and their dimension. (Hungarian), Diploma thesis, Babeş-Bolyai-University Cluj-Napoca, Romania, 2003.



2. I. PIOTROWSKA: Construction of Wavelets by means of multiscale analysis, and applications. (Polish), Diploma thesis, Adam-Mickiewicz- University Poznań, Poland, 2004.



3. B. VEDEL: Réglement de la divergence infra-rouge dans des bases d'ondelettes adaptées. (French), PhD thesis, Université de Picardie Jules Verne, France, 2004.



4. J. SCHNEIDER: Function spaces with varying smoothness, PhD thesis, FSU Jena, 2005.



5. E. TAMÁSI : Anisotropic function spaces, anisotropic fractals, and spectral theory for related fractal semi-elliptic operators, PhD thesis, FSU Jena, 2006.



6. I. PIOTROWSKA: Weighted function spaces and traces on fractals, PhD thesis, FSU Jena, 2006.

Papers

1. A.M. CAETANO, D.D. HAROSKE : Sharp estimates of approximation numbers via growth envelopes. Function spaces, differential operators and nonlinear analysis. The Hans Triebel Anniversary Volume. Proc. Conf. Teistungen, 2001 (ed. D.D. Haroske, Th. Runst, H.-J. Schmeißer), 237-244, Birkhäuser, Basel, 2003.



2. D.D. HAROSKE, S.D. MOURA : Continuity envelopes of spaces of generalised smoothness, entropy and approximation numbers. J. Approx. Theory, 128 (2), 151-174, 2004.



3. I. PIOTROWSKA: Image compression meets wavelets -- Standard JPEG 2000. Survey article, (Polish), Proc. VII International Workshop for Young Mathematicians on Applied Mathematics, Krakow, Poland, 2004.



4. A.M. CAETANO, D.D. HAROSKE : Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers. J. Function Spaces Appl., 33-71, 3(1), 2005.



5. D.D. HAROSKE, H. TRIEBEL : Wavelet bases and entropy numbers in weighted function spaces. Math. Nachr., 108-132, 278(1-2), 2005.



6. D.D. HAROSKE, E. TAMÁSI : Wavelet frames in anisotropic Besov spaces. Georgian Math. J., 637--658, 12(4), 2005.



7. E. TAMÁSI : Anisotropic Besov spaces and approximation numbers of traces on related fractal sets. Rev. Mat. Complut., 19 (2), 297-321, 2006.



8. I. PIOTROWSKA : Traces on fractals of function spaces with Muckenhoupt weights. Functiones et Approximatio, 36, 95-117, 2006.



9. D.D. HAROSKE: Growth envelope functions in Besov and Sobolev spaces. Local versus global results. Math. Nachr., 280(9-10), 1094-1107, 2007.



10. S.D. MOURA, I. PIOTROWSKA, M. PIOTROWSKI : Non-smooth atomic decompositions of anisotropic function spaces and some applications. Studia Math., 180(2), 169-190, 2007.



11. B. VEDEL : Besov Characteristic of a distribution. Rev. Mat. Complut., 20 (2), 407-421, 2007.



12. D.D. HAROSKE: Envelope functions in real interpolation spaces. A first approach. In: L. De Carli, M. Milman (ed.), Interpolation Theory and Applications, Contemp.Math., 445, pages 93–102. Proceedings of the Conference held in Miami, FL, March 29-31, 2006, AMS, Providence, RI., 2007.



13. J. SCHNEIDER : Function spaces of varying smoothness, I. Math. Nachr., 280(16), 1801-1826, 2007.



14. D.D. HAROSKE: Singularities in Muckenhoupt weighted function spaces. Banach Center Publ., 79, 95-112, 2007.



15. I. PIOTROWSKA: Entropy and approximation numbers of embeddings between weighted Besov spaces. Banach Center Publ., 79, 173-185, 2007.



16. J. SCHNEIDER : Some results on function spaces of varying smoothness. Banach Center Publ., 79, 187-195, 2007.



17. D.D. HAROSKE, I. PIOTROWSKA : Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis. Math. Nachr., to appear.

Preprints

1. D.D. HAROSKE, H. TRIEBEL : Wavelet bases and entropy numbers in weighted function spaces. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/04, Universität Jena, Germany, 2004.  



2. A.M. CAETANO, D.D. HAROSKE : Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/06/04, Universität Jena, Germany, 2004.  



3. D.D. HAROSKE, E. TAMÁSI : Wavelet frames in anisotropic Besov spaces. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/05, Universität Jena, Germany, 2005.  



4. D.D. HAROSKE, I. PIOTROWSKA : Atomic decompositions of function spaces with Muckenhoupt weights; an example from fractal geometry. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/06/05, Universität Jena, Germany, 2005.  



5. E. TAMÁSI : Approximation numbers of traces from anisotropic Besov spaces on anisotropic fractal $d$-sets. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/09/05, Universität Jena, Germany, 2005.  



6. B. VEDEL : Besov Characteristic of a distribution Jenaer Schriften zur Mathematik und Informatik, Math/Inf/10/05, Universität Jena, Germany, 2005.  



7. J. SCHNEIDER : Function spaces with negative and varying smoothness Jenaer Schriften zur Mathematik und Informatik, Math/Inf/02/06, Universität Jena, Germany, 2006.  



8. I. PIOTROWSKA : Traces on fractals of function spaces with Muckenhoupt weights. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/03/06, Universität Jena, Germany, 2006.  



9. S.D. MOURA, I. PIOTROWSKA, M. PIOTROWSKI : Non-smooth atomic decompositions of anisotropic function spaces and some applications. Technical Report 06-38, University of Coimbra, Portugal, 2006.  



10. D.D. HAROSKE, S.D. MOURA : Continuity envelopes and sharp embeddings in spaces of generalized smoothness. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/19/06, Universität Jena, Germany, 2006.