DOI: 10.1007/bf00336857. On representation and approximation of nonlinear systems

On representation and approximation of nonlinear systems

10.1007/bf00336857

Crossref journal-article

Springer Science and Business Media LLC

Biological Cybernetics (297)

Bibliography

Palm, G. (1979). On representation and approximation of nonlinear systems. Biological Cybernetics, 34(1), 49â52.

Authors 1

G. Palm (first)

References 13 Referenced 83

Dieudonn�, J.: Foundations of modern analysis. Berlin, Heidelberg, New York: Springer 1976 / Foundations of modern analysis by J. Dieudonn� (1976)
Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Providence: AMS 1957 / Functional analysis and semi-groups by E. Hille (1957)
Kolmogoroff, A.N.: On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition (russian). Dokl. Akad. Nauk SSSR 114, 953?956 (1957);
AMS Transl. 2, 55?59 (1963) (10.2307/3756381)
Lorentz, G.G.: Approximation of functions. New York: Holt, Rinehart, and Winston 1967 / Approximation of functions by G.G. Lorentz (1967)
Minsky, M., Papert, S.: Perceptrons. Cambridge, Mass.: MIT 1968 / Perceptrons by M. Minsky (1968)
Muroga, S.: Threshold logic and its applications. New York, London: Wiley and Sons 1971 / Threshold logic and its applications by S. Muroga (1971)
Palm, G., Poggio, T.: The Volterra representation and the Wiener expansion: Validity and pitfalls. SIAM J. Appl. Math. 33, 195?216 (1977) (10.1137/0133012) / SIAM J. Appl. Math. by G. Palm (1977)
Palm, G., Poggio, T.: Stochastic identification methods for nonlinear systems: an extension of the Wiener theory. SIAM J. Appl. Math. 34, 524?534 (1978) (10.1137/0134041) / SIAM J. Appl. Math. by G. Palm (1978)
Palm, G., Poggio, T.: Discrete system theory (in preparation)
Palm, G.: On representation and approximation of nonlinear systems. Biol. Cybernetics 31, 119?124 (1978) (10.1007/BF00344243) / Biol. Cybernetics by G. Palm (1978)
Sprecher, D.A.: An improvement in the superposition theorem of Kolmogorov. J. Math. Anal. Appl. 38, 208?213 (1972) (10.1016/0022-247X(72)90129-1) / J. Math. Anal. Appl. by D.A. Sprecher (1972)
Varj�, D.: Systemtheorie. Berlin, Heidelberg, New York: Springer 1978 / Systemtheorie by D. Varj� (1978)

Dates

Type	When
Created	20 years, 10 months ago (Oct. 27, 2004, 5:03 p.m.)
Deposited	5 years, 4 months ago (April 3, 2020, 10:03 a.m.)
Indexed	1 month, 1 week ago (July 22, 2025, 6:55 a.m.)
Issued	46 years, 8 months ago (Jan. 1, 1979)
Published	46 years, 8 months ago (Jan. 1, 1979)
Published Print	46 years, 8 months ago (Jan. 1, 1979)

Funders 0

None

BibTeX

@article{Palm_1979, title={On representation and approximation of nonlinear systems: Part II: Discrete time}, volume={34}, ISSN={1432-0770}, url={http://dx.doi.org/10.1007/bf00336857}, DOI={10.1007/bf00336857}, number={1}, journal={Biological Cybernetics}, publisher={Springer Science and Business Media LLC}, author={Palm, G.}, year={1979}, pages={49–52} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        22
      ]
    ],
    "date-time": "2025-07-22T10:55:26Z",
    "timestamp": 1753181726994
  },
  "reference-count": 13,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1979,
            1,
            1
          ]
        ],
        "date-time": "1979-01-01T00:00:00Z",
        "timestamp": 283996800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1979
      ]
    ]
  },
  "DOI": "10.1007/bf00336857",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        10,
        27
      ]
    ],
    "date-time": "2004-10-27T21:03:24Z",
    "timestamp": 1098911004000
  },
  "page": "49-52",
  "source": "Crossref",
  "is-referenced-by-count": 83,
  "title": "On representation and approximation of nonlinear systems",
  "prefix": "10.1007",
  "volume": "34",
  "author": [
    {
      "given": "G.",
      "family": "Palm",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "CR1",
      "volume-title": "Foundations of modern analysis",
      "author": "J. Dieudonn\ufffd",
      "year": "1976",
      "unstructured": "Dieudonn\ufffd, J.: Foundations of modern analysis. Berlin, Heidelberg, New York: Springer 1976"
    },
    {
      "key": "CR2",
      "volume-title": "Functional analysis and semi-groups",
      "author": "E. Hille",
      "year": "1957",
      "unstructured": "Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Providence: AMS 1957"
    },
    {
      "key": "#cr-split#-CR3.1",
      "unstructured": "Kolmogoroff, A.N.: On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition (russian). Dokl. Akad. Nauk SSSR 114, 953?956 (1957);"
    },
    {
      "key": "#cr-split#-CR3.2",
      "doi-asserted-by": "crossref",
      "unstructured": "AMS Transl. 2, 55?59 (1963)",
      "DOI": "10.2307/3756381"
    },
    {
      "key": "CR4",
      "volume-title": "Approximation of functions",
      "author": "G.G. Lorentz",
      "year": "1967",
      "unstructured": "Lorentz, G.G.: Approximation of functions. New York: Holt, Rinehart, and Winston 1967"
    },
    {
      "key": "CR5",
      "volume-title": "Perceptrons",
      "author": "M. Minsky",
      "year": "1968",
      "unstructured": "Minsky, M., Papert, S.: Perceptrons. Cambridge, Mass.: MIT 1968"
    },
    {
      "key": "CR6",
      "volume-title": "Threshold logic and its applications",
      "author": "S. Muroga",
      "year": "1971",
      "unstructured": "Muroga, S.: Threshold logic and its applications. New York, London: Wiley and Sons 1971"
    },
    {
      "key": "CR7",
      "doi-asserted-by": "crossref",
      "first-page": "195",
      "DOI": "10.1137/0133012",
      "volume": "33",
      "author": "G. Palm",
      "year": "1977",
      "unstructured": "Palm, G., Poggio, T.: The Volterra representation and the Wiener expansion: Validity and pitfalls. SIAM J. Appl. Math. 33, 195?216 (1977)",
      "journal-title": "SIAM J. Appl. Math."
    },
    {
      "key": "CR8",
      "doi-asserted-by": "crossref",
      "first-page": "524",
      "DOI": "10.1137/0134041",
      "volume": "34",
      "author": "G. Palm",
      "year": "1978",
      "unstructured": "Palm, G., Poggio, T.: Stochastic identification methods for nonlinear systems: an extension of the Wiener theory. SIAM J. Appl. Math. 34, 524?534 (1978)",
      "journal-title": "SIAM J. Appl. Math."
    },
    {
      "key": "CR9",
      "unstructured": "Palm, G., Poggio, T.: Discrete system theory (in preparation)"
    },
    {
      "key": "CR10",
      "doi-asserted-by": "crossref",
      "first-page": "119",
      "DOI": "10.1007/BF00344243",
      "volume": "31",
      "author": "G. Palm",
      "year": "1978",
      "unstructured": "Palm, G.: On representation and approximation of nonlinear systems. Biol. Cybernetics 31, 119?124 (1978)",
      "journal-title": "Biol. Cybernetics"
    },
    {
      "key": "CR11",
      "doi-asserted-by": "crossref",
      "first-page": "208",
      "DOI": "10.1016/0022-247X(72)90129-1",
      "volume": "38",
      "author": "D.A. Sprecher",
      "year": "1972",
      "unstructured": "Sprecher, D.A.: An improvement in the superposition theorem of Kolmogorov. J. Math. Anal. Appl. 38, 208?213 (1972)",
      "journal-title": "J. Math. Anal. Appl."
    },
    {
      "key": "CR12",
      "volume-title": "Systemtheorie",
      "author": "D. Varj\ufffd",
      "year": "1978",
      "unstructured": "Varj\ufffd, D.: Systemtheorie. Berlin, Heidelberg, New York: Springer 1978"
    }
  ],
  "container-title": "Biological Cybernetics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF00336857.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF00336857/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF00336857",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2020,
        4,
        3
      ]
    ],
    "date-time": "2020-04-03T14:03:18Z",
    "timestamp": 1585922598000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF00336857"
    }
  },
  "subtitle": [
    "Part II: Discrete time"
  ],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1979
      ]
    ]
  },
  "references-count": 13,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          1979
        ]
      ]
    }
  },
  "alternative-id": [
    "BF00336857"
  ],
  "URL": "http://dx.doi.org/10.1007/BF00336857",
  "relation": {},
  "ISSN": [
    "0340-1200",
    "1432-0770"
  ],
  "subject": [],
  "container-title-short": "Biol. Cybernetics",
  "published": {
    "date-parts": [
      [
        1979
      ]
    ]
  }
}