Kramers–Kronig relations
relations connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane
| rdfs:label |
"Kramers–Kronig relations"@en
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skos:alt |
"علاقه كراميرس-كرونيج"@ar
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| schema:description |
"relations connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane"@en
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schema:date |
"2026-09-06T13:44:36+00:00"^^xsd:dateTime |
| schema:version | 2541102526 |
| wikibase:identifiers | 5 |
| wikibase:sitelinks | 17 |
| wikibase:statements | 9 |
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| p:P2534 | wd:statement/Q1424764-a91e75a8-43ce-ae14-b3dd-a1bcc098ffe6 |
| p:P2924 | wd:statement/Q1424764-c26ae7d9-4e50-6c05-2143-350b5a5da13f |
| p:P31 | wd:statement/Q1424764-7fec4a60-4f7e-0f96-3154-ec6ad7f8dc14 |
| p:P5064 | wd:statement/Q1424764-332b7766-4a65-8619-7c66-773a46b14fec |
| p:P5555 | wd:statement/Q1424764-99aa6818-42a5-c60f-2192-c3e240d7d5b6 |
| p:P6366 | wd:statement/Q1424764-F99BF2BB-99FF-4E40-8C42-7EA200BDD816 |
| p:P646 | wd:statement/Q1424764-6DAB24FD-A187-4D45-8D72-79AF760AB42A |
|
p:direct- |
<https:/ |
| wdt:P10 |
<http:/ |
| wdt:P10283 | "C196224560" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mi mathvariant="normal">ℜ</mi><mi>χ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒫</mi></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ℑ</mi><mi>χ</mi><mo stretchy="false">(</mo><msup><mi>ω</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>ω</mi><mo>′</mo></msup><mo stretchy="false">−</mo><mi>ω</mi></mrow></mrow></mfrac></mrow><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><msup><mi>ω</mi><mo>′</mo></msup></mtd></mtr><mtr><mtd><mi mathvariant="normal">ℑ</mi><mi>χ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒫</mi></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ℜ</mi><mi>χ</mi><mo stretchy="false">(</mo><msup><mi>ω</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>ω</mi><mo>′</mo></msup><mo stretchy="false">−</mo><mi>ω</mi></mrow></mrow></mfrac></mrow><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><msup><mi>ω</mi><mo>′</mo></msup></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2924 | "2114286" |
| wdt:P31 | mathematical concept |
| wdt:P5064 | "Kronig-KramersRelations" |
| wdt:P5555 |
<http:/ |
| wdt:P6366 | "196224560" |
| wdt:P646 | "/m/07h050" |
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