References on Mathematical Analysis and its Applications
Here is a list of some references on
mathematical analysis and its applications
in which I am interested.
Integral Geometry and Geometric Tomography
original papers or surveys on basic ideas proposed by scientists
A. M. Cormack,
Representation of a function by its line integrals, with some radiological applications,
Journal of Applied physics,
34 (1963), pp.2722,
doi: 10.1063/1.1729798.
A. M. Cormack,
Representation of a function by its line integrals, with some radiological applications. II,
Journal of Applied physics,
35 (1964), pp.2908,
doi: 10.1063/1.1713127.
P. C. Lauterbur,
Image formation by induced local interactions: Examples employing nuclear magnetic resonance,
Nature,
242 (1973), pp.190--191,
doi: 10.1038/242190a0.
M. Cheney, D. Isaacson and J. C. Newell,
Electrical impedance tomography,
SIAM Review,
41 (1999), pp.85--101,
doi: 10.1137/S0036144598333613.
S. Helgason, "Integral Geometry and Radon Transforms",
Springer, 2011,
url.
G. Olafsson and E. T. Quinto eds,
"The Radon Transform, Inverse Problems, and Tomography",
Proceedings of Symposia in Applied Mathematics, 63,
American Mathematical Society, Providence, RI, 2006,
url.
F. Natterer and F. Wübbeling,
"Mathematical Methods in Image Reconstruction",
SIAM monographs on mathematical modeling and computation,
SIAM, 2001,
doi: 10.1137/1.9780898718324.
O. Scherzer eds,
"Handbook of Mathematical methods in Imaging",
Springer, 2015,
url,
contents.
V. Palamodov, "Reconstructive Integral Geometry",
Springer, 2004,
url.
V. Palamodov, "Reconstruction from Integral Data",
Chapman and Hall/CRC, 2016,
url.
R. J. Gardner,
"Geometric Tomograhy" Second Edition,
Encyclopedia of Mathematics and its Applications
58,
Cambridge University Press, 1995, 2006,
url.
mathematical papers
E. T. Quinto,
An introduction to X-ray tomography and Radon transforms,
"The Radon Transform, Inverse Problems, and Tomography",
Proceedings of Symposia in Applied Mathematics, 63, pp.1--23,
American Mathematical Society, Providence, RI, 2006,
url.
V. P. Krishnan and E. T. Quinto,
Microlocal analysis in tomography,
Handbook of mathematical methods in imaging. Vol. 1, 2, 3,
pp.847--902, Springer, New York, 2015,
pdf.
G. P. Patrnain, M. Salo and G. Uhlmann,
Tensor tomography: Progress and challenges,
Chinese Annales of Mathematics, Series B,
35 (2014), pp.399--428,
doi: 10.1007/s11401-014-0834-z.
P. Kuchment and L. Kunyansky,
Mathematics of thermoacoustic tomography,
European Journal of Applied Mathematics,
19 (2008), pp.191--224,
doi: 10.1017/S0956792508007353.
P. Kuchment and L. Kunyansky,
Mathematics of Photoacoustic and Thermoacoustic Tomography,
Handbook of mathematical methods in imaging. Vol. 1, 2, 3,
pp.1117--1167, Springer, New York, 2015,
arXiv:0912.2022.
geometry of convex bodies
A. Koldobsky,
"Fourier Analysis in Convex Geometry",
SURV 116,
American Mathematical Society, 2005,
url.
Microlocal Analysis and Geometry
Boutet de Monvel's calculus and index theory
E. Schrohe,
A short introduction to Boutet de Monvelâ€™s calculus,
Operator Theory: Advances and Applications,
125, pp.85-116, Springer, 2001,
doi: 10.1007/978-3-0348-8253-8_3,
pdf.
V. Nazaikinskii, B.-W. Schulze and B. Sternin,
"The Localization Problem in Index Theory of Elliptic Operators",
Pseudo=Differential Operators, 10, Birkhäuser, 2014,
doi: 10.1007/978-3-0348-0510-0.
semiclassical analysis and complex geometry
O. Rouby, J. Sjöstrand and S. V. Ngoc,
Analytic Bergman operators in the semiclassical limit,
arXiv:1808.00199.
analysis on generalized Heisenberg groups
A. Kable,
On certain conformally invariant systems of differential equations,
New York Journal of Mathematics,
19 (2013), pp.189--251,
url.
A. Kable,
On certain conformally invariant systems of differential equations II,
Tsukuba Journal of Mathematics,
39 (2015), pp.39--81,
doi:10.21099/tkbjm/1438951817.
analysis on the Poincaré disk
S. Zelditch,
Pseudodifferential analysis on hyperbolic surfaces,
J. Funct. Anal., 68 (1986), pp.72-105,
doi: 10.1016/0022-1236(86)90058-3.
W. Bauer and L. A. Coburn,
Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation,
J. Reine Angew. Math., 703 (2015), pp.225-246,
doi: 10.1515/crelle-2015-0016.
Applications of Euclidean Fourier Analysis, Differential Equations and etc
textbooks focusing on applications
B. G. Osgood,
"Lectures on the Fourier Transform and Its Applications",
Pure and Applied Undergraduate Texts, 33,
the American Mathematical Society, 2019,
url.
C. E. Shannon,
A mathematical theory of communication,
the Bell System Technical Journal,
27(4) (1948), pp.623-656,
doi: 10.1002/j.1538-7305.1948.tb00917.x.
C. E. Shannon,
Communication in the presence of noise,
Proceedings of the Institute of Radio Engineers,
37(1) (1949), pp.10-21,
doi: 10.1109/JRPROC.1949.232969,
pdf.
compressive sampling
E. J. Candes, J. K. Romberg and T. Tao,
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,
IEEE Transactions on Information Theory,
52 (2006), pp.489--509,
doi: 10.1109/TIT.2005.862083,
pdf.
E. J. Candes, J. K. Romberg and T. Tao,
Stable signal recovery from incomplete and inaccurate measurements,
Communications on Pure and Applied Mathematics,
59 (2006), pp.1207--1233,
doi: 10.1002/cpa.20124,
pdf.
E. J. Candes and T. Tao,
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?,
IEEE Transactions on Information Theory,
52 (2006), pp.5406--5425,
doi: 10.1109/TIT.2006.885507,
pdf.
spherical design
A. Bondarenko, D. Radchenko and M. Viazovska,
Optimal asymptotic bounds for spherical designs,
Annales of Mathematics,
178 (2013), pp.443-452,
doi: 10.4007/annals.2013.178.2.2,
pdf.
mobile communication
T. Strohmer,
Pseudodifferential operators and Banach algebras in mobile communications,
Applied and Computational Harmonic Analysis,
20 (2006), pp.237--249,
doi: 10.1016/j.acha.2005.06.003.
In this paper, mobile communication is formulated in terms of pseudodifferential operators of order zero, and some finite dimensional approximation is proposed.
Some academic journals and a useful webpage on image and signal processing.
M. W. Mahoney, J. C. Duchi and A. C. Gilbert eds,
"The Mathematics of Data",
IAS/Park City Mathematics Series, 25,
the American Mathematical Society, 2018,
url.
A. Bandeira,
Topics in Mathematics in Data Science 2015,
url.
A. Bandeira,
Mathematics of Data Science 2016,
url.
C. Jones,
Will climate change mathematics?
,
IMA Journal of Applied Mathematics,
76 (2011), pp.353--370,
doi: 10.1093/imamat/hxr018.
If you search "climate change" in
MathSciNet,
almost of all the results you meet are concerned with statistics.
This paper is based on partial differential equationsnot and not concerned with statistics.
Population Research
B. Perthame, "Transport Equations in Biology",
Birkhäuser, 2007,
url.
Model equations of age-structured population dynamics had been studied mainly from a poit of view of Japanese theory of evolution equations (i.e., semi-group theory). In contrast, this book gives an introductory course on mathematical analysis of these models by using French theory of evolution equations (i.e., duality). The requirements of readers are only calculus and linear algebra.
Immunology
J. K. Percus, "Mathematical Methods in Immunology",
American Mathematical Society, 2011,
url.
This book gives ordinary differential equations arising in immunology, and the analysis of them. The requirements of readers are only calculus and linear algebra.