Class information for:
Level 2: APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS//FRAMES//GABOR FRAMES

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
1602 7120 21.5 46%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
568 3       COMPUTER AIDED GEOMETRIC DESIGN//ISOGEOMETRIC ANALYSIS//COMPUTER-AIDED DESIGN 16883
1602 2             APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS//FRAMES//GABOR FRAMES 7120
4187 1                   MULTIWAVELETS//REFINEMENT EQUATION//REFINABLE FUNCTIONS 1831
4664 1                   GABOR FRAMES//MODULATION SPACES//FRAMES 1746
7734 1                   WAVELET GALERKIN METHOD//WAVELETS//TRIGONOMETRIC WAVELETS 1334
12574 1                   GENERALIZED SAMPLING//AVERAGE SAMPLING//SAMPLING THEOREM 896
17462 1                   SHEARLETS//CURVELETS//DIRECTIONAL WAVELETS 598
21484 1                   SELF AFFINE MEASURE//SPECTRAL PAIRS//ORTHOGONAL EXPONENTIALS 417
24884 1                   GENERAL FRANKLIN SYSTEM//INVERSE GRAM MATRIX//ITERATED CUBIC SPLINES 298

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS journal 701681 5% 43% 379
2 FRAMES authKW 627705 7% 29% 497
3 GABOR FRAMES authKW 602245 2% 91% 155
4 WAVELETS authKW 561016 12% 16% 827
5 SHIFT INVARIANT SPACES authKW 530080 2% 90% 138
6 MODULATION SPACES authKW 503056 2% 88% 134
7 MULTIWAVELETS authKW 477837 2% 77% 144
8 JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS journal 324630 4% 30% 254
9 MULTIRESOLUTION ANALYSIS authKW 289577 3% 32% 209
10 REFINABLE FUNCTIONS authKW 285356 1% 81% 82

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with term
in class
1 Mathematics, Applied 84844 43% 1% 3090
2 Mathematics 61094 40% 1% 2873
3 Physics, Mathematical 6525 9% 0% 644
4 Mathematics, Interdisciplinary Applications 3137 5% 0% 370
5 Engineering, Electrical & Electronic 2800 14% 0% 991
6 Computer Science, Software Engineering 1493 4% 0% 272
7 Computer Science, Information Systems 379 3% 0% 179
8 Engineering, General 231 2% 0% 136
9 Mechanics 229 3% 0% 217
10 Computer Science, Artificial Intelligence 181 2% 0% 139

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with term
in class
1 MATH 59468 34% 1% 2449
2 GEOMETRIE PRAKT MATH 50891 1% 26% 46
3 NUHAG 50200 0% 38% 31
4 MATH INFORMAT FB12 42867 0% 100% 10
5 COMPUTAT MATH SCI TECHNOL 37045 0% 79% 11
6 NUMER HARMON ANAL GRP NUHAG 34294 0% 100% 8
7 LEHRSTUHL NUMER MATH 28120 0% 41% 16
8 EUITT 27416 0% 40% 16
9 FB MATH INFORMAT 12 21001 0% 70% 7
10 MATH DIDACT MATH 19474 0% 45% 10

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 701681 5% 43% 379
2 JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 324630 4% 30% 254
3 INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 196091 2% 26% 174
4 JOURNAL OF APPROXIMATION THEORY 70212 3% 7% 237
5 CONSTRUCTIVE APPROXIMATION 51044 2% 11% 109
6 ADVANCES IN COMPUTATIONAL MATHEMATICS 46969 1% 16% 68
7 LECTURE NOTES IN PURE AND APPLIED MATHEMATICS 35337 1% 13% 63
8 IEEE TRANSACTIONS ON SIGNAL PROCESSING 23227 3% 2% 233
9 SIAM JOURNAL ON MATHEMATICAL ANALYSIS 13902 2% 3% 110
10 NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 12425 1% 4% 74

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 FRAMES 627705 7% 29% 497 Search FRAMES Search FRAMES
2 GABOR FRAMES 602245 2% 91% 155 Search GABOR+FRAMES Search GABOR+FRAMES
3 WAVELETS 561016 12% 16% 827 Search WAVELETS Search WAVELETS
4 SHIFT INVARIANT SPACES 530080 2% 90% 138 Search SHIFT+INVARIANT+SPACES Search SHIFT+INVARIANT+SPACES
5 MODULATION SPACES 503056 2% 88% 134 Search MODULATION+SPACES Search MODULATION+SPACES
6 MULTIWAVELETS 477837 2% 77% 144 Search MULTIWAVELETS Search MULTIWAVELETS
7 MULTIRESOLUTION ANALYSIS 289577 3% 32% 209 Search MULTIRESOLUTION+ANALYSIS Search MULTIRESOLUTION+ANALYSIS
8 REFINABLE FUNCTIONS 285356 1% 81% 82 Search REFINABLE+FUNCTIONS Search REFINABLE+FUNCTIONS
9 REFINEMENT EQUATION 284326 1% 93% 71 Search REFINEMENT+EQUATION Search REFINEMENT+EQUATION
10 SHEARLETS 251608 1% 76% 77 Search SHEARLETS Search SHEARLETS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 HEIL, C , (2007) HISTORY AND EVOLUTION OF THE DENSITY THEOREM FOR GABOR FRAMES.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. VOL. 13. ISSUE 2. P. 113 -166 97 93% 59
2 LI, B , CHEN, XF , (2014) WAVELET-BASED NUMERICAL ANALYSIS: A REVIEW AND CLASSIFICATION.FINITE ELEMENTS IN ANALYSIS AND DESIGN. VOL. 81. ISSUE . P. 14-31 86 64% 23
3 SCHNEIDER, K , VASILYEV, OV , (2010) WAVELET METHODS IN COMPUTATIONAL FLUID DYNAMICS.ANNUAL REVIEW OF FLUID MECHANICS. VOL. 42. ISSUE . P. 473 -503 73 69% 58
4 KUTYNIOK, G , (2007) AFFINE DENSITY IN WAVELET ANALYSIS - INTRODUCTION.AFFINE DENSITY IN WAVELET ANALYSIS. VOL. 1914. ISSUE . P. 1 -133 61 94% 0
5 GROCHENIG, K , (2014) THE MYSTERY OF GABOR FRAMES.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. VOL. 20. ISSUE 4. P. 865 -895 46 98% 5
6 UNSER, M , (2000) SAMPLING - 50 YEARS AFTER SHANNON.PROCEEDINGS OF THE IEEE. VOL. 88. ISSUE 4. P. 569 -587 55 75% 525
7 ATREAS, ND , PAPADAKIS, M , STAVROPOULOS, T , (2016) EXTENSION PRINCIPLES FOR DUAL MULTIWAVELET FRAMES OF CONSTRUCTED FROM MULTIREFINABLE GENERATORS.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. VOL. 22. ISSUE 4. P. 854 -877 44 100% 0
8 CASAZZA, PG , (2000) THE ART OF FRAME THEORY.TAIWANESE JOURNAL OF MATHEMATICS. VOL. 4. ISSUE 2. P. 129 -201 54 89% 202
9 ALDROUBI, A , GROCHENIG, K , (2001) NONUNIFORM SAMPLING AND RECONSTRUCTION IN SHIFT-INVARIANT SPACES.SIAM REVIEW. VOL. 43. ISSUE 4. P. 585 -620 48 83% 299
10 CASAZZA, PG , (2001) MODERN TOOLS FOR WEYL-HEISENBERG (GABOR) FRAME THEORY.ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL 115. VOL. 115. ISSUE . P. 1 -127 59 88% 18

Classes with closest relation at Level 2


Rank Class id link
1 3334 NEUTRIX LIMIT//COLOMBEAU ALGEBRA//BOEHMIANS
2 442 COMPRESSED SENSING//IMAGE DENOISING//IMAGE RESTORATION
3 1419 COMPUTER AIDED GEOMETRIC DESIGN//ISOGEOMETRIC ANALYSIS//COMPUTER-AIDED DESIGN
4 2845 VOLTERRA INTEGRAL EQUATION//WEAKLY SINGULAR KERNEL//BLOCK PULSE FUNCTIONS
5 2288 MODULUS OF CONTINUITY//JOURNAL OF APPROXIMATION THEORY//MODULUS OF SMOOTHNESS
6 1793 FRACTIONAL FOURIER TRANSFORM//MECHANICAL SYSTEMS AND SIGNAL PROCESSING//FAULT DIAGNOSIS
7 1037 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS//IEEE TRANSACTIONS ON SIGNAL PROCESSING//ADAPTIVE FILTERING
8 842 MATHEMATICS//MAXIMAL OPERATOR//BMO
9 3345 LEVEL CROSSING SAMPLING//SCI TECHNOL TELECOMMUN//CONSERVATIVE FLOW
10 3270 JOURNAL OF COMPLEXITY//QUASI MONTE CARLO METHODS//QUASI MONTE CARLO

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