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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.190191,
doi: 10.1038/242190a0.

M. Cheney, D. Isaacson and J. C. Newell,
Electrical impedance tomography,
SIAM Review,
41 (1999), pp.85101,
doi: 10.1137/S0036144598333613.

L. Borcea,
Electrical impedance tomography,
Inverse Problems,
18 (2002), pp.R99R136,
doi: 10.1088/02665611/18/6/201.
 integral geometry in Euclidean spaces

G. Beylkin,
The inversion problem and applications of the generalized radon transform,
Communications on Pure and Applied Mathematics, 37 (1984), pp.579599,
doi: 10.1002/cpa.3160370503.

R. J. Gardner,
"Geometric Tomograhy" Second Edition,
Encyclopedia of Mathematics and its Applications,
58,
Cambridge University Press, 1995, 2006,
url.

J. Frikel and E. T. Quinto,
Limited Data Problems for the Generalized Radon Transform in R^{n},
SIAM Journal on Mathematical Analysis, 48 (2016), pp.23012318,
doi: 10.1137/15M1045405.

S. Helgason, "Integral Geometry and Radon Transforms",
Springer, 2011,
url.

V. P. Krishnan and R. K. Mishra,
Microlocal Analysis of a Restricted Ray Transform on Symmetric mTensor Fields in R^{n},
SIAM Journal on Mathematical Analysis, 50 (2016), pp.62306254,
doi: 10.1137/18M1178530.

V. P. Krishnan and E. T. Quinto,
Microlocal analysis in tomography,
Handbook of mathematical methods in imaging. Vol. 1, 2, 3,
pp.847902, Springer, New York, 2015,
pdf.

R. G. Novikov,
An inversion formula for the attenuated Xray transformation,
Arkiv för Matematik, 40 (2002), pp.145167,
doi: 10.1007/BF02384507.

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.

V. Palamodov, "Reconstructive Integral Geometry",
Springer, 2004,
url.

V. Palamodov, "Reconstruction from Integral Data",
Chapman and Hall/CRC, 2016,
url.

E. T. Quinto,
Singularities of the XRay Transform and Limited Data Tomography in R^{2} and R^{3},
SIAM Journal on Mathematical Analysis, 24 (1993), pp.12151225,
doi: 10.1137/0524069.

E. T. Quinto,
An introduction to Xray tomography and Radon transforms,
"The Radon Transform, Inverse Problems, and Tomography",
Proceedings of Symposia in Applied Mathematics, 63, pp.123,
American Mathematical Society, Providence, RI, 2006,
url.

B. Rubin,
Overdetermined Transforms in Integral Geometry,
Complex Analysis and Dynamical Systems VI: Part 1: PDE, Differential Geometry, Radon Transform, pp.291313,
Contemporary Mathematics, 653, American Mathematical Society, 2015,
doi: 10.1090/conm/653.

B. Rubin, "Introduction to Radon Transforms, With Elements of Fractional Calculus and Harmonic Analysis",
Encyclopedia of Mathematics and its Applications,
160,
Cambridge University Press, 2015,
url.

P. Stefanov,
Semiclassical sampling and discretization of certain linear inverse problems,
arXiv:1811.01240.
 tensor tomography

G. P. Patrnain, M. Salo and G. Uhlmann,
Tensor tomography: Progress and challenges,
Chinese Annales of Mathematics, Series B,
35 (2014), pp.399428,
doi: 10.1007/s114010140834z.

J. Ilmavirta and F. Monard,
Integral geometry on manifolds with boundary and applications,
"The Radon Transform: The First 100 Years and Beyond" (Ronny Ramlau, Otmar Scherzer, eds.), de Gruyter, 2019,
arXiv:1806.06088.
 applied mathematics related to tomography

P. Kuchment and L. Kunyansky,
Mathematics of thermoacoustic tomography,
European Journal of Applied Mathematics,
19 (2008), pp.191224,
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.11171167, Springer, New York, 2015,
arXiv:0912.2022.

U. Langer et al eds,
Radon Series on Computational and Applied Mathematics,
de Gruyter.

F. Natterer and F. Wübbeling,
"Mathematical Methods in Image Reconstruction",
SIAM monographs on mathematical modeling and computation,
SIAM, 2001,
doi: 10.1137/1.9780898718324.

R. Ramlau and O. Scherzer eds,
"The Radon Transform  The First 100 Years and Beyond",
Radon Series on Computational and Applied Mathematics 22,
de Gruyter, 2019,
url.

O. Scherzer eds,
"Handbook of Mathematical methods in Imaging",
Springer, 2015,
url,
contents.

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.85116, Springer, 2001,
doi: 10.1007/9783034882538_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: 10.1007/9783034805100.

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.189251,
url.

A. Kable,
On certain conformally invariant systems of differential equations II,
Tsukuba Journal of Mathematics,
39 (2015), pp.3981,
doi:10.21099/tkbjm/1438951817.

analysis on the Poincaré disk

S. Zelditch,
Pseudodifferential analysis on hyperbolic surfaces,
J. Funct. Anal., 68 (1986), pp.72105,
doi: 10.1016/00221236(86)900583.

W. Bauer and L. A. Coburn,
Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation,
J. Reine Angew. Math., 703 (2015), pp.225246,
doi: 10.1515/crelle20150016.

Applications of Euclidean Fourier Analysis, Differential Equations and etc

textbooks focusing on applications

Shannon's celebrating papers:

C. E. Shannon,
A mathematical theory of communication,
the Bell System Technical Journal,
27(3) (1948), pp.379423,
doi: 10.1002/j.15387305.1948.tb01338.x,
pdf.

C. E. Shannon,
A mathematical theory of communication,
the Bell System Technical Journal,
27(4) (1948), pp.623656,
doi: 10.1002/j.15387305.1948.tb00917.x.

C. E. Shannon,
Communication in the presence of noise,
Proceedings of the Institute of Radio Engineers,
37(1) (1949), pp.1021,
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.489509,
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.12071233,
doi: 10.1002/cpa.20124,
pdf.

E. J. Candes and T. Tao,
NearOptimal Signal Recovery From Random Projections: Universal Encoding Strategies?,
IEEE Transactions on Information Theory,
52 (2006), pp.54065425,
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.443452,
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.237249,
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.

Mathematics for Data Science

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.

Climate Change

An organization
Mathematics and Climate Research Network
was established.
It has a Twitter account
@mathclimate.

C. Jones,
Will climate change mathematics?
,
IMA Journal of Applied Mathematics,
76 (2011), pp.353370,
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 agestructured population dynamics had been studied mainly from a poit of view of Japanese theory of evolution equations (i.e., semigroup 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.